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Question Number 1453 by 112358 last updated on 06/Aug/15 $$Showthat$$$$\underset{r=1}{\sum ^n}{e}^{rx}=\frac{e^x(e^{nx}-1)}{e^x-1}(\ast )$$$$if{e}^{rx}=cos\left(irx\right)-isin\left(irx\right)andx\ne 0.$$$$[Donottreat(\ast )asaGPto$$$$\left.{directly}\:{obtain}\:{the}\:{result}.\right]…

Question Number 66980 by Mr Jor last updated on 21/Aug/19 Commented by Mr Jor last updated on 21/Aug/19 $$Thefigureaboveisarightpyramid$$$$witharectangularbaseABCDand$$$$VOastheheight.$$$${The}\:{vectors}\:\boldsymbol{{AD}}=\boldsymbol{{a}},\boldsymbol{{AB}}=\boldsymbol{{b}}\:{and}\:\boldsymbol{{DV}}=\boldsymbol{{c}}…

Question Number 132514 by mohammad17 last updated on 14/Feb/21 Answered by guyyy last updated on 15/Feb/21 Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 1437 by 112358 last updated on 03/Aug/15 $$Letf\left(x\right)bearealvaluedfunction$$$$\mathrm{\forall }x\in \mathbb{R}.Determinethefollowing$$$$sums:$$$$\left(1\right)S_1\left(n\right)=\underset{r=1}{\sum ^n}{tan}^{-1}\left(rf\left(x\right)\right)$$$$\left(\mathrm{2}\right)\:{S}_{\mathrm{2}} \left({n}\right)=\underset{{r}=\mathrm{1}} {\overset{{n}} {\sum}}{sin}^{−\mathrm{1}}…

Question Number 132497 by mathocean1 last updated on 14/Feb/21 $$a,b\in \mathbb{R}.$$$$Given{a}^3+b^3-ab+11=0$$$$Showthat-\frac{7}{3}<a+b<-2$$ Answered by MJS_new last updated on 14/Feb/21…