Consider the function series $$f(x)=\sum_{n=1}^{\infty}\frac{1}{\sqrt{n}}-\frac{1}{\sqrt{n+x}}$$ According to some theorems, I found that the above series is convergent point wise on $(-1, +\infty)$. Does the series represent a well-known function?
2026-04-01 23:14:19.1775085259
Does the series $\sum_{n=1}^{\infty}\frac{1}{\sqrt{n}}-\frac{1}{\sqrt{n+x}}$ represent a well-known function?
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