Consider
Find
n=1
n=2
n=3
n=6
n=10
is that right?
First, use Partial Fractions to simplify .
If
.
Then
.
So and .
So .
Therefore .
So for your series:
.
Notice that if we expand this out...
Can you see that every term except for the first and last cancels?
So the sum is .
What do you think and equal?
P.S. A telescopic series is a series where everything except the first and last terms cancel.