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Author: Tinku Tara

mathematical-analysis-prove-that-1-0-1-ln-x-cos-2-pix-dx-ln-2pi-4-pi-8-2-lim-n-n-1-n-2-2-n-3-2-1-

Question Number 134079 by mnjuly1970 last updated on 27/Feb/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…..{mathematical}\:\:\:\:{analysis}….. \\ $$$$\:\:\:\:\:\:\:{prove}\:\:{that}:: \\ $$$$\:\:\:\:\:\:\:\mathrm{1}:\:\boldsymbol{\phi}=\int_{\mathrm{0}} ^{\:\mathrm{1}} {ln}\left(\Gamma\left({x}\right)\right){cos}^{\mathrm{2}} \left(\pi{x}\right){dx}=\frac{{ln}\left(\mathrm{2}\pi\right)}{\mathrm{4}}+\frac{\pi}{\mathrm{8}}\:..\checkmark \\ $$$$\:\:\:\:\:\:\mathrm{2}:\:\:{lim}_{{n}\rightarrow\infty} \frac{\Gamma\left({n}+\mathrm{1}\right)\Gamma\left({n}+\mathrm{2}\right)}{\Gamma^{\mathrm{2}} \left({n}+\frac{\mathrm{3}}{\mathrm{2}}\right)}\:=\mathrm{1}…\checkmark \\ $$ Answered by…

What-is-nth-term-1-2-5-4-15-8-37-16-83-32-

Question Number 3003 by Rasheed Soomro last updated on 02/Dec/15 $${What}\:{is}\:{nth}\:{term}? \\ $$$$\frac{\mathrm{1}}{\mathrm{2}},\frac{\mathrm{5}}{\mathrm{4}},\frac{\mathrm{15}}{\mathrm{8}},\frac{\mathrm{37}}{\mathrm{16}},\frac{\mathrm{83}}{\mathrm{32}}… \\ $$ Commented by Rasheed Soomro last updated on 05/Dec/15 $$\underset{−} {\mathcal{HIGH}{ly}}\:\mathcal{A}{ppriciate}\:\mathcal{Y}{our}\:\overset{\mathcal{VALUEABLE}}…

Question-68537

Question Number 68537 by naka3546 last updated on 13/Sep/19 Answered by MJS last updated on 13/Sep/19 $$\mathrm{1}\:\mathrm{8}\:\mathrm{17} \\ $$$$\mathrm{4}\:\mathrm{7}\:\mathrm{17} \\ $$$$\mathrm{4}\:\mathrm{13}\:\mathrm{13} \\ $$$$\mathrm{7}\:\mathrm{7}\:\mathrm{16} \\ $$$$\mathrm{8}\:\mathrm{11}\:\mathrm{13}…

Given-a-b-and-c-are-real-numbers-and-a-lt-b-lt-c-If-1-a-1-b-1-c-1-18-find-minimum-value-of-a-

Question Number 134069 by john_santu last updated on 27/Feb/21 $${Given}\:{a},{b}\:{and}\:{c}\:{are}\:{real}\:{numbers}\:{and}\:{a}<{b}<{c}. \\ $$$${If}\:\frac{\mathrm{1}}{{a}}\:+\:\frac{\mathrm{1}}{{b}}\:+\:\frac{\mathrm{1}}{{c}}\:=\:\frac{\mathrm{1}}{\mathrm{18}}\:,\:{find}\:{minimum}\:{value}\:{of}\:{a}. \\ $$ Commented by mr W last updated on 27/Feb/21 $${no}\:{minimum}\:{for}\:{a}\:{exists}. \\ $$…