The task is to find the sum of the series:
I can calculate the sum of an ordinary positive number series, but as I understand it, this series is not an ordinary positive number series. Tell me how to calculate the sum of such series
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Please do not use pictures for critical portions of your post. Pictures may not be legible, cannot be searched and are not view-able to some, such as those who use screen readers. – For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to. – Martin R Nov 15 '21 at 09:11
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What is an “ordinary positive number series”? How is this related to Fourier series? – Martin R Nov 15 '21 at 09:11
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I meant positive series – Ben Nov 15 '21 at 09:12
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Many similar questions have already been answered here. – Kavi Rama Murthy Nov 15 '21 at 09:13
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Have a look at https://math.stackexchange.com/q/3950025/42969 for a very similar question. – Martin R Nov 15 '21 at 09:13
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But I don't understand their answers. I did not understand why they got such answers and I decided to ask my own question. – Ben Nov 15 '21 at 09:14
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Then I suggest that you tell us which answers you have seen, and what you do not understand about them. Otherwise the question might get closed as a duplicate, or as off-topic (no context given), or you might get another answer which you do not understand. – Martin R Nov 15 '21 at 09:16
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Let's say the example from the link above, I don't understand why he expanded the series like that. How he in the first and in the second pulls out $8x$ or $2x^2$ – Ben Nov 15 '21 at 09:18