Question

Find the nth partial sum for a_n = 1/(n+1) - 1/(n+2)

Answer 1

put n=0,
1/1-1/2
put n=1,
1/2 -1/3
put n=2,
1/3-1/4
:
:
:
nth term =
1/(n+1) - 1/(n+2)

sum of n terms =
(1/1-1/2)+(1/2 -1/3)+(1/3-1/4)+...+1/(n+1) - 1/(n+2)
^ ^ ^ ^
|______| |______|
cancelled cancelled
=1-1/(n+2)