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Author: Tinku Tara

If-n-gt-1-prove-by-mathematical-induction-that-n-n-1-1-n-1-lt-1-1-2-1-3-1-4-1-n-

Question Number 5513 by 314159 last updated on 17/May/16 $${If}\:{n}>\mathrm{1},\:{prove}\:{by}\:{mathematical}\:{induction}\:{that} \\ $$$${n}\left(\left({n}+\mathrm{1}\right)^{\frac{\mathrm{1}}{{n}}} −\mathrm{1}\right)\:<\:\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{3}}+\frac{\mathrm{1}}{\mathrm{4}}+…\frac{\mathrm{1}}{{n}}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com

advanced-calculus-pove-that-n-0-1-n-2-2n-2n-n-cos-nx-cos-x-4-2cos-x-2-

Question Number 136581 by mnjuly1970 last updated on 23/Mar/21 $$\:\:\:\:\:\:\:\:…….{advanced}\:\:\:{calculus}…. \\ $$$$\:\:\:{pove}\:{that}:: \\ $$$$:::\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\left\{\frac{\left(−\mathrm{1}\right)^{{n}} }{\mathrm{2}^{\mathrm{2}{n}} }\begin{pmatrix}{\:\mathrm{2}{n}}\\{\:\:{n}}\end{pmatrix}\:{cos}\left({nx}\right)\right\}=\frac{{cos}\left(\frac{{x}}{\mathrm{4}}\right)}{\:\sqrt{\mathrm{2}{cos}\left(\frac{{x}}{\mathrm{2}}\right)}} \\ $$ Answered by Dwaipayan Shikari last…

Use-De-Moivre-s-theorem-to-prove-that-r-0-cos-rx-1-2-and-find-a-value-or-expression-for-r-0-sin-rx-assume-that-this-two-series-were-convergent-

Question Number 136582 by physicstutes last updated on 23/Mar/21 $$\mathrm{Use}\:\mathrm{De}'\mathrm{Moivre}'\mathrm{s}\:\mathrm{theorem}\:\mathrm{to}\:\mathrm{prove}\:\mathrm{that} \\ $$$$\:\underset{{r}=\mathrm{0}} {\overset{\infty} {\sum}}\mathrm{cos}\:{rx}\:=\:\frac{\mathrm{1}}{\mathrm{2}}\:\mathrm{and}\:\mathrm{find}\:\mathrm{a}\:\mathrm{value}\left(\mathrm{or}\:\mathrm{expression}\right)\:\mathrm{for}\:\underset{{r}=\mathrm{0}} {\overset{\infty} {\sum}}\mathrm{sin}\:{rx} \\ $$$$\mathrm{assume}\:\mathrm{that}\:\mathrm{this}\:\mathrm{two}\:\mathrm{series}\:\mathrm{were}\:\mathrm{convergent}. \\ $$ Answered by Ar Brandon last…

if-x-1-x-1-3x-x-2-ax-2-bx-c-then-a-b-c-

Question Number 5507 by Kasih last updated on 17/May/16 $${if}\:\left({x}−\mathrm{1}\right)\:\left({x}+\mathrm{1}\right)\:+\mathrm{3}{x}+{x}^{\mathrm{2}} ={ax}^{\mathrm{2}} +{bx}+{c}\:{then}\:{a}=?\:{b}=?\:{c}=? \\ $$ Answered by Rasheed Soomro last updated on 17/May/16 $$\:\left({x}−\mathrm{1}\right)\:\left({x}+\mathrm{1}\right)\:+\mathrm{3}{x}+{x}^{\mathrm{2}} ={ax}^{\mathrm{2}} +{bx}+{c}…