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Question Number 197005 by MrGHK last updated on 06/Sep/23

Answered by MathematicalUser2357 last updated on 10/Sep/23

$$\underset{n=0}{\sum ^{\mathrm{\infty }}}\frac{{(-1)}^n}{n}(\psi \left(\frac{an+2}{2}\right)-\psi \left(\frac{an+1}{2}\right))$$$$=\left(\frac{{(-1)}^0}{0}(\psi \left(\frac{\cancel{a\cdot 0}+2}{2}\right)-\psi \left(\frac{\cancel{a\cdot 0}+1}{2}\right))\right)+\cdot \cdot \cdot$$$$\mathrm{Division}\mathrm{by}0\mathrm{does}\mathrm{not}\mathrm{exist}$$$$\mathrm{So}\mathrm{this}\mathrm{is}\mathrm{divergent}$$

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