Reciprocals of odd squares Given that (Exercises 57 and

Chapter 10, Problem 59AE

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QUESTION:

Reciprocals of odd squares Given that \(\sum_{k=1}^{\infty} \frac{1}{k^{2}}=\frac{\pi^{2}}{6}\) (Exercises 57 and 58) and that the terms of this series may be rearranged without changing the value of the series. Determine the sum of the reciprocals of the squares of the odd positive integers.

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QUESTION:

Reciprocals of odd squares Given that \(\sum_{k=1}^{\infty} \frac{1}{k^{2}}=\frac{\pi^{2}}{6}\) (Exercises 57 and 58) and that the terms of this series may be rearranged without changing the value of the series. Determine the sum of the reciprocals of the squares of the odd positive integers.

ANSWER:

Solution:-

Step1

Given that

Step2

To find

 Determine the sum of the reciprocals of the squares of the odd positive integers.

Step3

We know that

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