Mathematics Thread

[CheesecakeCuber]

It doesn't alternate between 1 and another number. There are only 2 cases where (k^2)/(2^k)=1 --> k^2=2^k --> k=2, 4. (http://www.youtube.com/watch?v=mLQNvuZH3GU). So it goes 1/2, 1, 9/8, 1, 25/32, 36/64, 49/128, ....
After the first 2 terms (1/2, 1) the terms decrease, but with no common ratio (decimal approximations: 0.5, 1, 1.125, 1, .75, .54, .36, ....)

Haha oops, my mistake. I did carry it out a couple more terms and realized that.

Edit: And I'm insane enough to carry it out even more. So, yes, the answer's 6, except my proof would be showing terms until the 640th term.

 

[brandbest1]

Wait a sec, I just did that problem a few days ago!

Try multiplying by the common ratio. If you know what an arithmetico-geometric series is, then that's the approach you should take.

 

[CheesecakeCuber]

Wait a sec, I just did that problem a few days ago!

Try multiplying by the common ratio. If you know what an arithmetico-geometric series is, then that's the approach you should take.

I would if there was a common ratio! (Forgive me if I'm wrong and missing something big here)

 

[CheesecakeCuber]

I do this when I should be studying for midterms...why am I so addicted?

 

[KongShou]

I do this when I should be studying for midterms...why am I so addicted?

Omg thats an amazing site!

 

[TDM]

So apparently not everything only needs 4 questions for you to continue... this is going to take a while.

 

[CheesecakeCuber]

Alright, well in a feeble attempt to revive this thread and all the great things that used to (and still should) happen in it. I'd like to ask if anyone else here is interested in Riemann's Hypothesis and the distribution of primes shenanigans. I've recently gotten into researching and learning about the Riemann-Zeta Function and I've been reading Prime Obsession by John Derbyshire. Feel free to share whatever about this problem interests you.

 

[5BLD]

Try making a complex plane plotter in python (using colours to indicate abs/arg). Then plot the zeta function. S'very cool.

 

[10461394944000]

Alright, well in a feeble attempt to revive this thread and all the great things that used to (and still should) happen in it. I'd like to ask if anyone else here is interested in Riemann's Hypothesis and the distribution of primes shenanigans. I've recently gotten into researching and learning about the Riemann-Zeta Function and I've been reading Prime Obsession by John Derbyshire. Feel free to share whatever about this problem interests you.

i proved the riemann hypothesis last night then realized my proof was wrong like 2 minutes later

http://bit.ly/1r8ezw2

 

[CheesecakeCuber]

Here's a little Python implementation of the Riemann-Zeta function that takes the sum up to a certain term. It takes two arguments: n and x, where n is the nth term of the sum and x is the exponent argument (i.e., Zeta(x) = 1/n^x). Please tell me if there's anything that should change style wise or mistake wise.

Spoiler

def Zeta(n,x):
    #Where n is the nth term that you want to sum the function to
    #and x is the exponent
    n = int(n)
    x = int(x)
    if n < 1:
        return 'Error'
    if x < 1:
        return 'Error'
    if n == 1:
        return '1'
    else:
        n = int(n)
        x = int(x)
        return str((1 + sum(1.0/(n**x) for n in range(2, n+1))))

while True:
    userInputN = raw_input('Define n: ')
    print
    userInputX = raw_input('Define x: ')
    print
    print 'The sum is: ' + Zeta(userInputN, userInputX)
    print

 

[vcuber13]

    if x == 1:
        return 1 + 1.0/n

Why?

 

[CheesecakeCuber]

    if x == 1:
        return 1 + 1.0/n

Why?

Ouch, my mistake. I think I confused the variables. Thanks for pointing that out. I fixed the main post.

 

[ilikecubing]

How do I solve this simply?

Peter reaches school everyday at 5PM to pick up his child. On Saturday, the school got over at 4PM and the child started walking towards home. Peter met him on his way and returned home 30 minutes earlier. How long did the child walk?

 

[cmhardw]

How do I solve this simply?

Peter reaches school everyday at 5PM to pick up his child. On Saturday, the school got over at 4PM and the child started walking towards home. Peter met him on his way and returned home 30 minutes earlier. How long did the child walk?

I am very interested in this problem, but I have some clarification questions:

1) Does school typically get out at 4PM on a weekday? Or does getting out at 4PM on Saturday represent getting out at 1 hour earlier than is typical for a weekday?

2) When they travel home together, how do they travel home?

2a) When Peter picks up his child, do they travel together at Peter's original rate of travel? In regular terms you would say, for example, that Peter picks up the child in a car, and they drive home together.

2b) If Peter is also walking, then by the time Peter meets his child do they travel at the child's rate of travel? For example, an adult can walk faster than a child. However, when an adult and a child walk together the adult will typically slow to the child's rate of travel.

2c) Do they travel at some rate slower than Peter's original rate, yet faster than the child's rate? A real world example would be something like Peter carrying the child on his back. He would walk slower than his rate without the child, but probably still faster than the child can walk.

2d) Do they travel together at a rate slower than the child's rate? For example, do they stop to get ice cream, or walk very slowly such as to also carry on a meaningful conversation?

All of the part 2 question parts are basically me asking at what rate do they travel when they have met up and are now traveling, together, toward home? We don't necessarily need to know this rate exactly, but the mode of travel they take together can affect the answer to the whole problem.

 

[ilikecubing]

I am very interested in this problem, but I have some clarification questions:

1) Does school typically get out at 4PM on a weekday? Or does getting out at 4PM on Saturday represent getting out at 1 hour earlier than is typical for a weekday?

2) When they travel home together, how do they travel home?

2a) When Peter picks up his child, do they travel together at Peter's original rate of travel? In regular terms you would say, for example, that Peter picks up the child in a car, and they drive home together.

2b) If Peter is also walking, then by the time Peter meets his child do they travel at the child's rate of travel? For example, an adult can walk faster than a child. However, when an adult and a child walk together the adult will typically slow to the child's rate of travel.

2c) Do they travel at some rate slower than Peter's original rate, yet faster than the child's rate? A real world example would be something like Peter carrying the child on his back. He would walk slower than his rate without the child, but probably still faster than the child can walk.

2d) Do they travel together at a rate slower than the child's rate? For example, do they stop to get ice cream, or walk very slowly such as to also carry on a meaningful conversation?

All of the part 2 question parts are basically me asking at what rate do they travel when they have met up and are now traveling, together, toward home? We don't necessarily need to know this rate exactly, but the mode of travel they take together can affect the answer to the whole problem.

1) No, it does not get typically over at 4PM on weekends. It just happened to get over at 4 PM that saturday. So we have to assume that on that saturday, the child started walking towards his home right at 4 PM

2) When Peter meets the walking child and they start traveling back home, they travel together at the same rate as Peter's usual rate of traveling.

Btw, this problem has options. They are,

1) 40 min
2) 50 min
3) 45 min
4) 55 min
5) 60 min

 

[KongShou]

How do I solve this simply?

Peter reaches school everyday at 5PM to pick up his child. On Saturday, the school got over at 4PM and the child started walking towards home. Peter met him on his way and returned home 30 minutes earlier. How long did the child walk?

1) No, it does not get typically over at 4PM on weekends. It just happened to get over at 4 PM that saturday. So we have to assume that on that saturday, the child started walking towards his home right at 4 PM

2) When Peter meets the walking child and they start traveling back home, they travel together at the same rate as Peter's usual rate of traveling.

Btw, this problem has options. They are,

1) 40 min
2) 50 min
3) 45 min
4) 55 min
5) 60 min

Peter effectively walks to meet the child and walks back again. The duration of each half of Peters journey is the time the child walks for.

Now assume that Peter walks for x mins from school each day normally. This means that it took Peter x+30 mins to walk to meet the child and back that Saturday. Therefore the child traveled by himself for (x+30)/2 mins that day.

However we don't know the value of x so I can't see a way to solve the problem, as the value of x vary, so does the final answer??? This question seem to be incomplete imo. Maybe I'm just being stupid.

BTW where did you find this question?

 

[Methuselah96]

How do I solve this simply?

Peter reaches school everyday at 5PM to pick up his child. On Saturday, the school got over at 4PM and the child started walking towards home. Peter met him on his way and returned home 30 minutes earlier. How long did the child walk?

30 minutes earlier than what?

 

[Tempus]

How do I solve this simply?

Peter reaches school everyday at 5PM to pick up his child. On Saturday, the school got over at 4PM and the child started walking towards home. Peter met him on his way and returned home 30 minutes earlier. How long did the child walk?

• We may not know the speed at which Peter travels to pick up his child, but we do know that when the child started walking home an hour earlier than usual, i.e. at 4PM, it resulted in Peter arriving at home a half-hour earlier than usual.
• Assuming Peter was traveling from home and not some other location, and further assuming level ground, symmetrical traffic conditions, and no significant prevailing wind, this means that Peter's trip toward his child was 15 minutes shorter than usual, and their trip back home together was also 15 minutes shorter than usual.
• If Peter's trip toward his child was 15 minutes shorter than usual, and it usually ends at 5PM, then today Peter met up with his child at 4:45PM.
• If the child began walking at 4:00PM and was picked up by Peter at 4:45PM, the child was obviously walking for 45 minutes.

 

[KongShou]

• We may not know the speed at which Peter travels to pick up his child, but we do know that when the child started walking home an hour earlier than usual, i.e. at 4PM, it resulted in Peter arriving at home a half-hour earlier than usual.
• Assuming Peter was traveling from home and not some other location, and further assuming level ground, symmetrical traffic conditions, and no significant prevailing wind, this means that Peter's trip toward his child was 15 minutes shorter than usual, and their trip back home together was also 15 minutes shorter than usual.
• If Peter's trip toward his child was 15 minutes shorter than usual, and it usually ends at 5PM, then today Peter met up with his child at 4:45PM.
• If the child began walking at 4:00PM and was picked up by Peter at 4:45PM, the child was obviously walking for 45 minutes.

Nowhere is it mentioned how long it takes them to walk home. It does not usually end at 5pm.

Peter took 30 mins LONGER than usual. Since they left 1 hour early but only returned home 30 mins early.

This question is quite unclear in many aspects.

 

[Methuselah96]

Nowhere is it mentioned how long it takes them to walk home. It does not usually end at 5pm.

Peter took 30 mins LONGER than usual. Since they left 1 hour early but only returned home 30 mins early.

This question is quite unclear in many aspects.

How could it take 30 mins longer if he's walking the same rate with less distance?