Question Number 134269 by I want to learn more last updated on 01/Mar/21 $$\underset{\mathrm{k}\:\:\:=\:\:\:\:\mathrm{2}} {\overset{\mathrm{99}} {\sum}}\:\:\:\frac{\mathrm{k}^{\mathrm{2}} \:\:+\:\:\mathrm{1}}{\mathrm{k}^{\mathrm{2}} \:\:−\:\:\mathrm{1}} \\ $$ Answered by mr W last…
Question Number 68721 by ahmadshah last updated on 15/Sep/19 Commented by Prithwish sen last updated on 15/Sep/19 $$\mathrm{3} \\ $$ Answered by $@ty@m123 last updated…
Question Number 134255 by shaker last updated on 01/Mar/21 Commented by Dwaipayan Shikari last updated on 01/Mar/21 $${C}_{{m}} ^{{n}} \:\:\:\:\:\left({n}<{m}\right)\:{is}\:{not}\:{defined} \\ $$ Commented by mr…
Question Number 134237 by mathlove last updated on 01/Mar/21 $${f}\left({x}\right)=\frac{\mathrm{2}{x}^{\mathrm{100}!} }{\left(\mathrm{100}!\right)!}+{x}^{\mathrm{100}} +\mathrm{1} \\ $$$${faind}\:\:\:\:\:\frac{{d}^{\mathrm{100}!} {f}\left({x}\right)}{{dx}^{\mathrm{100}!} }=? \\ $$ Answered by malwan last updated on 01/Mar/21…
Question Number 3143 by Rasheed Soomro last updated on 06/Dec/15 $$\mathcal{S}{uggest}\:{minimum}\:{number}\:{of}\:{weights}\:{by}\:{which}\:{we}\:\:{can}\: \\ $$$${weigh}\:\:{upto}\:\mathrm{40}\:{kgs}\left({in}\:{whole}\:{numbers}\right)\:{in}\:{a}\:{traditional}\:{balance}. \\ $$$${If}\:{possible}\:{mention}\:{the}\:{process}\:{also}. \\ $$ Commented by Rasheed Soomro last updated on 06/Dec/15…
Question Number 3113 by Yozzi last updated on 05/Dec/15 $${Define},\:{for}\:{sets}\:{A}\:{and}\:{B}, \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{A}\ast{B}=\left({A}−{B}\right)\cup\left({B}−{A}\right). \\ $$$${Show}\:{that}\:{A}\ast{B}=\left({A}\cup{B}\right)−\left({A}\cap{B}\right). \\ $$$${Prove}\:{that}\:{A}\ast\left({B}\ast{C}\right)=\left({A}\ast{B}\right)\ast{C}.\: \\ $$ Commented by Yozzi last updated on 06/Dec/15…
Question Number 68636 by ajfour last updated on 14/Sep/19 $$\frac{−{a}^{\mathrm{2}} +{a}+\mathrm{1}}{\:\:\:\:{a}^{\mathrm{2}} +{a}+\mathrm{1}}=\frac{−{b}^{\mathrm{2}} +{b}+\mathrm{1}}{\:\:\:\:{b}^{\mathrm{2}} +{b}+\mathrm{1}} \\ $$$$\:\:=\:\frac{\:\:\:\:\mathrm{2}{a}^{\mathrm{2}} −\mathrm{2}{ab}+\left({b}−{a}\right)}{−\mathrm{2}{a}^{\mathrm{2}} +\mathrm{2}{ab}+\left({b}−{a}\right)} \\ $$$$\:\:=\frac{−\mathrm{2}{ab}+\left({a}+{b}\right)+\mathrm{2}}{\:\:\:\:\mathrm{2}{ab}+\left({a}+{b}\right)+\mathrm{2}} \\ $$$${Solve}\:{for}\:\boldsymbol{{a}}. \\ $$$$ \\…
Question Number 68624 by TawaTawa last updated on 14/Sep/19 Answered by Rasheed.Sindhi last updated on 14/Sep/19 $$\mathbb{A}\:\mathbb{T}\boldsymbol{\mathrm{ricky}}\:\mathbb{A}\boldsymbol{\mathrm{pproach}} \\ $$$$\mathrm{k}=−\mathrm{3}\left(\frac{\mathrm{1}}{\mathrm{a}^{\mathrm{2}} −\mathrm{a}+\mathrm{1}}+\frac{\mathrm{1}}{\mathrm{b}^{\mathrm{2}} −\mathrm{b}+\mathrm{1}}\right)+\mathrm{c} \\ $$$$\:\:=−\mathrm{3}\left(\frac{\mathrm{a}+\mathrm{1}}{\left(\mathrm{a}+\mathrm{1}\right)\left(\mathrm{a}^{\mathrm{2}} −\mathrm{a}+\mathrm{1}\right)}+\frac{\mathrm{b}+\mathrm{1}}{\left(\mathrm{b}+\mathrm{1}\right)\left(\mathrm{b}^{\mathrm{2}} −\mathrm{b}+\mathrm{1}\right)}\right)+\mathrm{c}…
Question Number 134134 by mr W last updated on 28/Feb/21 $$\mathrm{If}\:\mathrm{cos}^{−\mathrm{1}} {x}_{\mathrm{1}} +\mathrm{cos}^{−\mathrm{1}} {x}_{\mathrm{2}} +…+\mathrm{cos}^{−\mathrm{1}} {x}_{{n}} ={n}\pi, \\ $$$$\mathrm{then}\:\:{x}_{\mathrm{1}} \:+\:{x}_{\mathrm{2}} ^{\mathrm{2}} \:+\:{x}_{\mathrm{3}} ^{\mathrm{3}} \:+\:…+\:{x}_{{n}} ^{{n}}…
Question Number 3061 by Rasheed Soomro last updated on 04/Dec/15 $$\mathrm{Determine}\:\:\mathrm{nth}\:\:\mathrm{term}\:\mathrm{of}\:\mathrm{the}\:\mathrm{following}\:\mathrm{sequence} \\ $$$$\mathrm{1},\mathrm{0},−\mathrm{1},\mathrm{0},\mathrm{7},\mathrm{28},\mathrm{79},… \\ $$ Commented by prakash jain last updated on 04/Dec/15 $${one}\:{techinque}\:{is}\:{to}\:{define} \\…