Menu Close

Category: Relation and Functions

let-S-n-1-1-3-2-1-3-3-1-3-n-calculate-lim-n-S-n-

Question Number 41517 by maxmathsup by imad last updated on 08/Aug/18 $${let}\:\:{S}_{{n}} =\:\mathrm{1}\:+\frac{\mathrm{1}}{\left(^{\mathrm{3}} \sqrt{\mathrm{2}}\right)}\:+\:\frac{\mathrm{1}}{\left(^{\mathrm{3}} \sqrt{\mathrm{3}}\right)}\:+\:….+\frac{\mathrm{1}}{\left(^{\mathrm{3}} \sqrt{{n}}\right)} \\ $$$${calculate}\:{lim}\:_{{n}\rightarrow+\infty} \:{S}_{{n}} \\ $$ Commented by maxmathsup by…

let-u-n-1-1-3-1-2-3-1-n-3-1-prove-that-9-8-1-2-n-1-2-u-n-3-2-1-2n-2-2-prove-that-n-N-1-u-n-3-2-3-prove-that-u-n-is-convegente-

Question Number 41512 by maxmathsup by imad last updated on 08/Aug/18 $${let}\:\:{u}_{{n}} =\frac{\mathrm{1}}{\mathrm{1}^{\mathrm{3}} }\:+\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{3}} }\:+….+\frac{\mathrm{1}}{{n}^{\mathrm{3}} } \\ $$$$\left.\mathrm{1}\right){prove}\:{that}\:\:\:\frac{\mathrm{9}}{\mathrm{8}}\:−\frac{\mathrm{1}}{\mathrm{2}\left({n}+\mathrm{1}\right)^{\mathrm{2}} }\:\leqslant\:{u}_{{n}} \leqslant\:\frac{\mathrm{3}}{\mathrm{2}}\:−\frac{\mathrm{1}}{\mathrm{2}{n}^{\mathrm{2}} } \\ $$$$\left.\mathrm{2}\right)\:{prove}\:{that}\:\forall\:{n}\in{N}^{\bigstar} \:\:\:\mathrm{1}\leqslant{u}_{{n}} \leqslant\:\frac{\mathrm{3}}{\mathrm{2}}…