Question

find the nth partial sum Sn of the telescoping series and use it to determine whether the series converges or diverges. If it converges find its sum. The sum of n= 2 going to infinity (1/n-1 - 1/n)

Answer 1

1/(2-1) - 1/2
1/(3-1) - 1/3
1/(4-1) - 1/4
1/(5-1) - 1/5


1/1 - 1/2
1/2 - 1/3
1/3 - 1/4
1/4 - 1/5
... - 1/n


1 - 1/n is the nth partial sum

Answer 2

or another way to write it is:

n-1
----
n