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Author: Tinku Tara

1-find-a-and-b-wich-verify-0-pi-at-2-bt-cos-nx-1-n-2-2-find-the-value-of-n-1-1-n-2-

Question Number 82286 by mathmax by abdo last updated on 19/Feb/20 $$\left.\mathrm{1}\right)\:{find}\:{a}\:{and}\:{b}\:{wich}\:{verify}\:\:\int_{\mathrm{0}} ^{\pi} \left({at}^{\mathrm{2}} \:+{bt}\right){cos}\left({nx}\right)\:=\frac{\mathrm{1}}{{n}^{\mathrm{2}} } \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{value}\:{of}\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\frac{\mathrm{1}}{{n}^{\mathrm{2}} } \\ $$ Commented by…

Let-H-be-orthocenter-of-ABC-and-O-its-circumcenter-Prove-that-the-vectors-OA-OB-OC-and-OH-satisfy-the-following-equality-OA-OB-OC-OH-

Question Number 16748 by Tinkutara last updated on 26/Jun/17 $$\mathrm{Let}\:{H}\:\mathrm{be}\:\mathrm{orthocenter}\:\mathrm{of}\:\Delta{ABC}\:\mathrm{and}\:{O} \\ $$$$\mathrm{its}\:\mathrm{circumcenter}.\:\mathrm{Prove}\:\mathrm{that}\:\mathrm{the}\:\mathrm{vectors} \\ $$$$\overset{\rightarrow} {{OA}},\:\overset{\rightarrow} {{OB}},\:\overset{\rightarrow} {{OC}}\:\mathrm{and}\:\overset{\rightarrow} {{OH}}\:\mathrm{satisfy}\:\mathrm{the} \\ $$$$\mathrm{following}\:\mathrm{equality}: \\ $$$$\overset{\rightarrow} {{OA}}\:+\:\overset{\rightarrow} {{OB}}\:+\:\overset{\rightarrow} {{OC}}\:=\:\overset{\rightarrow}…

x-3-x-3-1-dx-

Question Number 82283 by M±th+et£s last updated on 19/Feb/20 $$\int{x}^{\mathrm{3}} \sqrt{{x}^{\mathrm{3}} +\mathrm{1}}\:{dx} \\ $$ Commented by MJS last updated on 20/Feb/20 $$\mathrm{it}'\mathrm{s}\:\mathrm{impossible}\:\mathrm{for}\:\mathrm{me}\:\mathrm{to}\:\mathrm{solve}\:\mathrm{this} \\ $$ Commented…

p-0-n-ch-2-a-pb-

Question Number 147819 by puissant last updated on 23/Jul/21 $$\underset{\mathrm{p}=\mathrm{0}} {\overset{\mathrm{n}} {\sum}}\mathrm{ch}^{\mathrm{2}} \left(\mathrm{a}+\mathrm{pb}\right) \\ $$ Answered by Olaf_Thorendsen last updated on 23/Jul/21 $$\mathrm{S}\:=\:\underset{{p}=\mathrm{0}} {\overset{{n}} {\sum}}\mathrm{ch}^{\mathrm{2}}…