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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!

 Feb 22, 2022
 #1
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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

 Feb 22, 2022
 #3
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thank you!! this really helped!!

Guest Feb 22, 2022
 #2
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sumfor(n, 1, infinity, 6 / ((2*n + 1)^2 - 1))==converges to 3/2 ==1.5

 Feb 22, 2022

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