- #1

Felipe Lincoln

Gold Member

- 99

- 11

## Homework Statement

Find the sum of ##\sum\limits_{n=2}^{\infty}\ln\left(1-\dfrac{1}{n^2}\right) ##

## Homework Equations

No one.

## The Attempt at a Solution

At first I though it as a telescopic serie:

##\sum\limits_{n=2}^{\infty}\ln\left(1-\dfrac{1}{n^2}\right) =\ln\left(\dfrac{3}{4}\right) + \ln\left(\dfrac{8}{9}\right) + \ln\left(\dfrac{15}{16}\right) + \dots < 0##

But it doesn't look like so.

we know from it's terms that ##s_n## is in the interval of ##(L, \ln\left(3/4\right)]##