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Reciprocals of odd squares Given that (Exercises 57 and
Chapter 10, Problem 59AE(choose chapter or problem)
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.
Questions & Answers
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