Obviously, this converges but I do not understand how it converges to 1/2, which

Question

Obviously, this converges but I do not understand how it converges to 1/2, which is the confirmed answer, your help is greatly appreciated.

This is exercise 28 of Section 8.2 page 512.

For the following series, if it converges, enter the sum. If not, enter DIV.

Obviously, this converges but I do not understand how it converges to 1/2, which is the confirmed answer, your help is greatly appreciated. For the following series, if it converges, enter the sum. If not, enter DIV. 1 / (2k - 1) (2k + 1)

Explanation / Answer

the complete question please

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