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
