Respuestas

2012-09-09T22:30:12+02:00
After playing with this a little, it looks like:
1/(n-1)n(n+1) = 
(1/2) [1/(n-1)n - 1/n(n+1)]

So the sum is:
(1/2)[(1/1*2 - 1/2*3) + (1/2*3 - 1/3*4) + ... 
+ (1/100*101 - 1/101*102)] =

(1/2)[1/1*2 - 1/101*102] =
1/4 - 1/20604 6 years ago