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Author: Tinku Tara

Study-the-convergence-with-respect-to-and-the-improper-integral-below-0-dx-x-lnx-

Question Number 143755 by Ar Brandon last updated on 18/Jun/21 $$\mathrm{Study}\:\mathrm{the}\:\mathrm{convergence}\:\mathrm{with}\:\mathrm{respect}\:\mathrm{to} \\ $$$$\alpha\:\mathrm{and}\:\beta\:\mathrm{the}\:\mathrm{improper}\:\mathrm{integral}\:\mathrm{below}; \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{dx}}{\mathrm{x}^{\alpha} \left(\mathrm{lnx}\right)^{\beta} } \\ $$ Answered by mathmax by…

Question-143751

Question Number 143751 by help last updated on 17/Jun/21 Answered by TheHoneyCat last updated on 17/Jun/21 $$\mathrm{let}\:{R}_{\mathrm{0}} ={r} \\ $$$$\mathrm{I}\:\mathrm{will}\:\mathrm{right}\:{R}_{{ijk}} \:\mathrm{for}\:\mathrm{the}\:\mathrm{total}\:\mathrm{resistance}\:\mathrm{of}\:{i},{j}\:\mathrm{and}\:{k}… \\ $$$$ \\ $$$${R}_{\mathrm{34}}…

Prove-that-lim-n-2n-2n-1-ln-n-p-0-n-ln-1-p-2-ln-e-pi-e-pi-

Question Number 143740 by Willson last updated on 17/Jun/21 $$\mathrm{Prove}\:\mathrm{that} \\ $$$$\underset{\mathrm{n}\rightarrow+\infty} {\mathrm{lim}2n}−\left(\mathrm{2n}+\mathrm{1}\right)\mathrm{ln}\left(\mathrm{n}\right)+\underset{\mathrm{p}=\mathrm{0}} {\overset{\mathrm{n}} {\sum}}\mathrm{ln}\left(\mathrm{1}+\mathrm{p}^{\mathrm{2}} \right)=\:\mathrm{ln}\left({e}^{\pi} −{e}^{−\pi} \right) \\ $$ Answered by TheHoneyCat last updated…