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Question-66979

Question Number 66979 by Mr Jor last updated on 21/Aug/19 Commented by Mr Jor last updated on 21/Aug/19 $${In}\:{the}\:{figure}\:{above},\:{OC}=\mathrm{3}{CA}\:{and} \\ $$$${OD}=\mathrm{3}{DB}.{By}\:{taking}\:\boldsymbol{{OA}}=\boldsymbol{{a}},\boldsymbol{{OB}} \\ $$$$=\boldsymbol{{b}},{show}\:{that}\:{CB}//{AB}. \\ $$…

Let-f-x-be-a-real-valuedfunction-x-R-Determine-the-following-sums-1-S-1-n-r-1-n-tan-1-rf-x-2-S-2-n-r-1-n-sin-1-rf-x-f-x-1-n-3-S-3-n-r-1-n-cos-1-

Question Number 1437 by 112358 last updated on 03/Aug/15 $${Let}\:{f}\left({x}\right)\:{be}\:{a}\:{real}\:{valuedfunction} \\ $$$$\forall{x}\in\mathbb{R}.\:{Determine}\:{the}\:{following} \\ $$$${sums}\:: \\ $$$$\left(\mathrm{1}\right)\:{S}_{\mathrm{1}} \left({n}\right)=\underset{{r}=\mathrm{1}} {\overset{{n}} {\sum}}{tan}^{−\mathrm{1}} \left({rf}\left({x}\right)\right) \\ $$$$\left(\mathrm{2}\right)\:{S}_{\mathrm{2}} \left({n}\right)=\underset{{r}=\mathrm{1}} {\overset{{n}} {\sum}}{sin}^{−\mathrm{1}}…

why-we-can-not-compare-any-tow-complex-number-how-a-cmplex-number-is-uses-a-complex-number-practically-please-giveanexample-

Question Number 1426 by tabrez8590@gmail last updated on 31/Jul/15 $${why}\:{we}\:{can}\:{not}\:{compare}\:{any}\:{tow}\:{complex}\:{number}\:\: \\ $$$${how}\:{a}\:{cmplex}\:{number}\:{is}\:{uses}\:{a}\:{complex}\:{number}\:{practically}\:{please}\:{giveanexample} \\ $$ Commented by Rasheed Ahmad last updated on 03/Aug/15 $${Things}\:{with}\:{respect}\:{to}\:{single}\: \\ $$$${characteristic}\:{are}\:{easy}\:{to}\:{compare}.…

P-n-1-999-1-2n-1-2n-Q-n-1-999-1-999-n-1999-n-P-Q-

Question Number 66910 by naka3546 last updated on 20/Aug/19 $${P}\:\:=\:\:\underset{{n}=\mathrm{1}} {\overset{\mathrm{999}} {\sum}}\:\frac{\mathrm{1}}{\left(\mathrm{2}{n}−\mathrm{1}\right)\left(\mathrm{2}{n}\right)} \\ $$$${Q}\:\:=\:\:\underset{{n}=\mathrm{1}} {\overset{\mathrm{999}} {\sum}}\:\frac{\mathrm{1}}{\left(\mathrm{999}+{n}\right)\left(\mathrm{1999}−{n}\right)} \\ $$$$\frac{{P}}{{Q}}\:\:=\:\:? \\ $$ Commented by naka3546 last updated…