Math Problem - 14

[nitrocan]

Simplify 1/2! + 2/3! + 3/4! + ... + 99/100!

[Tim Reynolds]

Spoiler:

The nth term is n/(n+1)! = ((n+1)-1)/(n+1)! = (n+1)/(n+1)! - 1/(n+1)! = 1/n!-1/(n+1)!. So we can write this as

(1/1!-1/2!)+(1/2!-1/3!)+(1/3!-1/4!)+...+(1/99!-1/100!)
=1 + (-1/2!+1/2!) + (-1/3!+1/3!)+...+(-1/99!+1/99!) - 1/100!

all terms in parentheses are zero, so we are left with 1-1/100!

[nitrocan]

I need to find some harder problems!

[Stefan]

Or you could start talking about cubing.

[badmephisto]

Or you could start talking about cubing.

That's dangerously On-Topic