Question Number 4285 by Filup last updated on 07/Jan/16 $${S}=\mathrm{1}+\sqrt{\mathrm{2}+\sqrt{\mathrm{3}+\sqrt{\mathrm{4}+…}}} \\ $$$${S}=??? \\ $$ Commented by RasheedSindhi last updated on 07/Jan/16 $$\mathrm{S}=\sqrt{\mathrm{2}+\sqrt{\mathrm{3}+\sqrt{\mathrm{4}+…}}} \\ $$$${S}\left({n}\right)=\sqrt{\left({n}+\mathrm{1}\right)+{S}\left({n}+\mathrm{1}\right)} \\…
Question Number 4092 by Filup last updated on 28/Dec/15 $$\mathrm{Prove}: \\ $$$$\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\frac{{n}!}{\left({n}−{k}\right)!\:{k}!}=\mathrm{2}^{{n}} −\mathrm{1} \\ $$ Answered by Yozzii last updated on 28/Dec/15 $${According}\:{to}\:{the}\:{Binomial}\:{Theorem},…
Question Number 4066 by Filup last updated on 27/Dec/15 $$\mathrm{Can}\:\mathrm{we}\:\mathrm{prove}\:\pi\:\mathrm{is}\:\mathrm{tracendental}? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 69557 by aliesam last updated on 24/Sep/19 Answered by MJS last updated on 24/Sep/19 $${x}=\mathrm{72} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 3928 by Filup last updated on 24/Dec/15 $$\mathrm{Is}\:\mathrm{this}\:\mathrm{solvable}: \\ $$$$ \\ $$$${y}=\lfloor{f}\left({x}\right)\rfloor\:\:\:\:\:\:\:\:\:\mathrm{floor}\:\mathrm{function} \\ $$$$\frac{{dy}}{{dx}}=??? \\ $$ Commented by Yozzii last updated on 25/Dec/15…
Question Number 3929 by Filup last updated on 25/Dec/15 $$\mathrm{For}: \\ $$$${S}=\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{3}}+…+\frac{\mathrm{1}}{{n}} \\ $$$${S}={H}_{{n}} \:\:\:\:{Harmonic}\:{sequence} \\ $$$${H}_{{n}} =\underset{{i}=\mathrm{1}} {\overset{{n}} {\sum}}\frac{\mathrm{1}}{{i}} \\ $$$${Can}\:{you}\:{solve}\:{the}\:{partial}\:{sum}? \\ $$ Commented…
Question Number 69393 by 06 last updated on 23/Sep/19 Commented by Prithwish sen last updated on 23/Sep/19 $$\left(\mathrm{3}^{\mathrm{t}} +\mathrm{3}^{−\mathrm{t}} \right)^{\mathrm{3}} =\:\mathrm{5}^{\mathrm{3}} \Rightarrow\mathrm{27}^{\mathrm{t}} +\mathrm{27}^{−\mathrm{t}} +\mathrm{3}.\mathrm{3}^{\mathrm{t}} .\mathrm{3}^{−\mathrm{t}}…
Question Number 3794 by Filup last updated on 21/Dec/15 $$\mathrm{prove}\:\mathrm{or}\:\mathrm{disprove}:\:\:\:\:\:\underset{{i}=\mathrm{1}} {\overset{{n}} {\sum}}{p}_{\mathrm{1}} {i}={p}_{\mathrm{2}} \\ $$$${p}_{\mathrm{1}} ,{p}_{\mathrm{2}} \in\mathbb{P} \\ $$$$ \\ $$$$\frac{\mathrm{1}}{\mathrm{2}}{np}_{\mathrm{1}} \left({n}+\mathrm{1}\right)={p}_{\mathrm{2}} \\ $$$$\frac{\mathrm{1}}{\mathrm{2}}{n}\left({n}+\mathrm{1}\right)=\frac{{p}_{\mathrm{2}} }{{p}_{\mathrm{1}}…
Question Number 69175 by Aditya789 last updated on 21/Sep/19 $${if}\:{two}\:{finite}\:{sets}\:{have}\:{m}\:{and}\:{n}\:{term}.{if}\:{the}\:{no}\:{of}\:{subset}\:{of}\:{first}\:{set}\:{is}\:\mathrm{112}\:{more}\:{then}\:{the}\:{no}\:{of}\:{subset}\:{of}\:{second}\:{set}.{find}\:{m}\:{and}\:{n}? \\ $$ Answered by Rasheed.Sindhi last updated on 21/Sep/19 $$\mid\mathrm{A}\mid={m}\:,\:\mid\mathrm{B}\mid={n} \\ $$$$\mathrm{P}\left(\mathrm{A}\right)=\mathrm{2}^{{m}} \:,\:\mathrm{P}\left(\mathrm{B}\right)=\mathrm{2}^{{n}} \\ $$$$\mathrm{P}\left(\mathrm{A}\right)−\mathrm{P}\left(\mathrm{B}\right)=\mathrm{2}^{{m}}…
Question Number 3628 by madscientist last updated on 16/Dec/15 $${if}\:{the}\:{fibonacci}\:{sequence}\:{is}\: \\ $$$$\mathrm{1},\mathrm{1},\mathrm{2},\mathrm{3},\mathrm{5},\mathrm{8},\mathrm{13},\mathrm{21},\mathrm{34}… \\ $$$${where}\:{it}\:{is}\:\mathrm{1}+\mathrm{1}=\mathrm{2},\:\mathrm{2}+\mathrm{3}=\mathrm{5},\:\mathrm{3}+\mathrm{5}=\mathrm{8},… \\ $$$${how}\:{can}\:{we}\:{represent}\:{this}\:{sequence}\: \\ $$$${in}\:{summitation}\:{notation}\:\Sigma \\ $$$${or}\:{product}\:{notation}\:\Pi? \\ $$ Commented by 123456…