Category: Arithmetic

Question Number 121949 by liberty last updated on 12/Nov/20 $$\mathrm{Evaluate}\mathrm{the}\mathrm{sum}\frac{2}{3+1}+\frac{2^2}{3^2+1}+\frac{2^3}{3^4+1}+\dots +\frac{2^{\mathrm{n}+1}}{3^{2^{\mathrm{n}}}+1}.$$ Answered by bobhans last updated on…

Question Number 121832 by bemath last updated on 12/Nov/20 $$Let\{\begin{array}{l}{u}_1=1\\ u_2=1\end{array}and{u}_{n+2}=u_{n+1}+u_n$$$$find{u}_n.$$ Commented by bemath last updated on…

Question Number 187235 by Rupesh123 last updated on 15/Feb/23 Commented by MJS_new last updated on 15/Feb/23 $$\mathrm{I}\mathrm{believe}{\mathrm{it}}^{\prime }\mathrm{s}3$$ Commented by Rasheed.Sindhi last updated on…

Question Number 121568 by mathocean1 last updated on 09/Nov/20 $$\mathrm{Given}:\mathrm{N}\mathrm{in}\mathrm{base}10\mathrm{is}$$$$158\mathrm{b}687\mathrm{a}\mathrm{where}\mathrm{b}\mathrm{and}\mathrm{a}\mathrm{are}$$$$\mathrm{digits}(\mathrm{a}<\mathrm{b}).\mathrm{Given}:$$$$\mathrm{N}\equiv 2+\mathrm{a}\left[4\right].$$$$1)\mathrm{Determinate}\mathrm{couples}$$$$(\mathrm{a};\mathrm{b})\mathrm{such}\mathrm{that}11\mathrm{divise}\mathrm{N}.$$$$2)\mathrm{Determinate}\mathrm{couples}(\mathrm{a};\mathrm{b})$$$$\mathrm{such}\:\mathrm{that}\:\mathrm{3}\:\mathrm{and}\:\mathrm{25}\:\mathrm{divise}\:\mathrm{N}. \…

Question Number 187085 by Rupesh123 last updated on 13/Feb/23 Answered by witcher3 last updated on 14/Feb/23 $${\mathrm{S}}_{\mathrm{n}}=\underset{\mathrm{k}=1}{\sum ^{\mathrm{n}}}\frac{1}{\mathrm{n}+\mathrm{k}}$$$$\mathrm{S}_{\mathrm{n}+\mathrm{1}} −\mathrm{S}_{\mathrm{n}} =\underset{\mathrm{k}=\mathrm{1}} {\overset{\mathrm{n}+\mathrm{1}}…