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

sum_(n=1)^∞ 6/((2 n + 1)^2 - 1) = 3/2

Can you please explain how you got to that answer, and it is correct btw thanks!

The computer simply sums up all these fractions and get 3/2:

0.75 0.25 0.125 0.075 0.05 0.0357142857 1 0.0267857142 9 0.0208333333 3 0.0166666666 7 0.0136363636 4 .

.

............etc.

Could you also please answer this question?

The sum of the first $n$ terms of a certain sequence is $n(n + 1)(n + 2).$ Find the tenth term of the sequence.