Consider

Find

n=1

n=2

n=3

n=6

n=10

is that right?

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- May 8th 2010, 11:33 PMAnemoriTelescoping sum of series
Consider

Find

n=1

n=2

n=3

n=6

n=10

is that right? - May 9th 2010, 12:11 AMProve It
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. - May 9th 2010, 10:31 AMAnemori
- May 9th 2010, 02:38 PMProve It