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

 Feb 14, 2020
 #1
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+1

sum_(n=1)^∞ 6/((2 n + 1)^2 - 1) = 3/2

 Feb 14, 2020
 #2
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+2

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

Guest Feb 14, 2020
 #3
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+1

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.

Guest Feb 14, 2020
 #4
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+2

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.

Guest Feb 14, 2020

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