Evaluate the sum \(\dfrac{6}{3^2-1}+\dfrac{6}{5^2-1}+\dfrac{6}{7^2-1}+\dfrac{6}{9^2-1}+\cdots\)

any help will be appreciated!

thank you!

The steps to solve an infinite sum are as follows:

1. Generalize the sum with a variable. example: 1/(n(n+1))

2. Partial fraction decomposition

3. Plug in values, of n=1, 2, 3

4. Notice the pattern and cancel out the terms

thank you!! this really helped!!

sumfor(n, 1, infinity, 6 / ((2*n + 1)^2 - 1))==converges to 3/2 ==1.5