Relation and Functions – Page 50

prove-that-n-1-ax-1-n-pi-a-n-lim-x-1-a-1-n-1-cotan-pix-n-1-

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Question Number 108688 by abdomsup last updated on 18/Aug/20 $p r o v e t h a t$ $\sum_{n = - \infty}^{\infty} \frac{1}{{(a x + 1)}^{n}}$ $= - \frac{π}{a^{n}} {l i m}_{x \to - \frac{1}{a}} \frac{1}{(n - 1)!} {c o t a n (π x)}^{(n - 1)}$ Commented by mathdave last…

Solve-the-following-equation-cosz-2-

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Question Number 108547 by 1549442205PVT last updated on 17/Aug/20 $Solve the following equation :$ $cosz = 2$ Answered by mr W last updated on 17/Aug/20 $${e}^{{zi}} =\mathrm{cos}\:{z}+{i}\:\mathrm{sin}\:{z} \…

calculate-A-n-k-0-n-k-C-n-k-B-n-k-0-n-k-2-C-n-k-C-n-k-0-n-k-3-C-n-k-

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Question Number 43007 by abdo.msup.com last updated on 06/Sep/18 $c a l c u l a t e$ $A_{n} = \sum_{k = 0}^{n} k C_{n}^{k}$ $B_{n} = \sum_{k = 0}^{n} k^{2} C_{n}^{k}$ $${C}_{{n}}…

prove-that-k-1-n-1-1-k-gt-1-k-1-n-1-k-

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Question Number 43001 by abdo.msup.com last updated on 06/Sep/18 $p r o v e t h a t \prod_{k = 1}^{n} (1 + \frac{1}{k}) > 1 + \sum_{k = 1}^{n} \frac{1}{k}$ Answered by tanmay.chaudhury50@gmail.com last updated on 06/Sep/18 $${LHS} \…

let-u-n-1-i-lt-j-n-1-ij-1-find-a-equivalent-of-u-n-2-calculate-lim-n-u-n-

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Question Number 43003 by abdo.msup.com last updated on 06/Sep/18 $l e t u_{n} = \sum_{1 ⩽ i < j ⩽ n} \frac{1}{\sqrt{i j}}$ $1) f i n d a e q u i v a l e n t o f u_{n}$ $2) c a l c u l a t e {l i m}_{n \to + \infty} u_{n}$ Answered by maxmathsup by imad last…

prove-that-2-2-2-2cos-pi-2-n-

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Question Number 43000 by abdo.msup.com last updated on 06/Sep/18 $p r o v e t h a t \sqrt{2 + \sqrt{2 + \dots . + \sqrt{2}}} = 2 c o s (\frac{π}{2^{n}})$ Answered by tanmay.chaudhury50@gmail.com last updated on 06/Sep/18 $c o s 2 α = 2 {c o s}^{2} α - 1$ $${cos}^{\mathrm{2}} \alpha=\frac{\mathrm{1}+{cos}\mathrm{2}\alpha}{\mathrm{2}}…

let-f-x-x-1-x-1-1-calculate-f-n-2-2-if-f-x-n-0-a-n-x-2-n-find-the-sequence-a-n-

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Question Number 42999 by abdo.msup.com last updated on 06/Sep/18 $l e t f (x) = \sqrt{x} + \frac{1}{x - 1}$ $1) c a l c u l a t e f^{(n)} (2)$ $2) i f f (x) = \sum_{n = 0}^{\infty} a_{n} {(x - 2)}^{n} f i n d t h e$ $s e q u e n c e a_{n}$ Commented by…

calculate-lim-n-S-n-with-S-n-1-n-4-k-1-n-k-3-1-k-n-2-3-

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Question Number 42805 by maxmathsup by imad last updated on 02/Sep/18 $c a l c u l a t e {l i m}_{n \to + \infty} S_{n} w i t h$ $S_{n} = \frac{1}{n^{4}} \sum_{k = 1}^{n} \frac{k^{3}}{\sqrt{{(1 + {(\frac{k}{n})}^{2})}^{3}}}$ …

let-u-0-1-and-u-n-1-u-n-2-u-n-study-the-convervence-of-u-n-

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Question Number 42789 by maxmathsup by imad last updated on 02/Sep/18 $l e t u_{0} = 1 a n d u_{n + 1} = u_{n} + \frac{2}{u_{n}}$ $s t u d y t h e c o n v e r v e n c e o f (u_{n})$ Commented by maxmathsup by…

calculate-lim-x-0-2x-ln-1-x-1-x-cosx-

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Question Number 42788 by maxmathsup by imad last updated on 02/Sep/18 $c a l c u l a t e {l i m}_{x \to 0} \frac{2 x}{l n (\frac{1 + x}{1 - x})} - c o s x$ Commented by maxmathsup by imad last updated on 30/Sep/18 $${we}\:{have}\:\frac{\mathrm{2}{x}}{{ln}\left(\frac{\mathrm{1}+{x}}{\mathrm{1}−{x}}\right)}\:=\frac{\mathrm{2}{x}}{{ln}\left(\mathrm{1}+{x}\right)−{ln}\left(\mathrm{1}−{x}\right)}\:{but}…

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