Number Theory – Page 57

Evaluate-sin-n-n-From-1-to-infinity-

Tinku Tara June 3, 2023 Number Theory 0 Comments

Question Number 7189 by Tawakalitu. last updated on 15/Aug/16 $E v a l u a t e : Σ \frac{s i n (n)}{n}, F r o m 1 t o i n f i n i t y .$ Commented by Yozzia last updated on 15/Aug/16 $${f}\left({x}\right)=\frac{{a}_{\mathrm{0}} }{\mathrm{2}}+\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\left\{{a}_{{n}} {cos}\frac{{n}\pi{x}}{{L}}+{b}_{{n}} {sin}\frac{{n}\pi{x}}{{L}}\right\}…

Is-u-n-real-sequence-defende-by-u-0-3e-t-u-n-1-2-u-n-2-1-Determine-the-general-term-u-n-of-this-series-justify-your-answer-and-method-used-

Tinku Tara June 3, 2023 Number Theory 0 Comments

Question Number 7005 by Tawakalitu. last updated on 05/Aug/16 $I s u_{n} r e a l s e q u e n c e d e f e n d e b y$ $u_{0} = 3 e^{t} u_{n + 1} = 2 {(u_{n})}^{2} - 1$ $D e t e r m i n e t h e g e n e r a l t e r m u_{n} o f t h i s s e r i e s$ $(j u s t i f y y o u r a n s w e r a n d m e t h o d u s e d)$ $$…

Question-138003

Tinku Tara June 3, 2023 Number Theory 0 Comments

Question Number 138003 by benjo_mathlover last updated on 09/Apr/21 Answered by EDWIN88 last updated on 09/Apr/21 $b e g i n f r o m \underset{n = 1}{\sum^{\infty}} \frac{x^{n}}{n!} = e^{x} - 1 . T a k i n g d e r i v a t i v e$ $$\Rightarrow\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{nx}^{{n}−\mathrm{1}}…

Question-137635

Tinku Tara June 3, 2023 Number Theory 0 Comments

Question Number 137635 by Dwaipayan Shikari last updated on 04/Apr/21 Commented by Dwaipayan Shikari last updated on 04/Apr/21 $A f r i e n d o f m i n e s e n t m e t h i s . I a m p o s t i n g t h i s b e h a l f o f$ $h i m$ Terms of…

Find-the-cube-of-the-number-N-7-3-7-3-7-3-7-3-

Tinku Tara June 3, 2023 Number Theory 0 Comments

Question Number 137585 by bramlexs22 last updated on 04/Apr/21 $F i n d t h e c u b e o f t h e n u m b e r$ $N = \sqrt{7 \sqrt{3 \sqrt{7 \sqrt{3 \sqrt{7 \sqrt{3 \sqrt{7 \sqrt{3 \dots}}}}}}}}$ Answered by bemath last updated on 04/Apr/21 $N = 7^{\frac{1}{2} + \frac{1}{8} + \frac{1}{32} + \frac{1}{128} + \dots} . 3^{\frac{1}{4} + \frac{1}{16} + \frac{1}{64} + \dots}$ $${N}=\mathrm{7}^{\frac{\mathrm{1}/\mathrm{2}}{\mathrm{1}−\mathrm{1}/\mathrm{4}}}…

1-1-pi-i-

Tinku Tara June 3, 2023 Number Theory 0 Comments

Question Number 137579 by liberty last updated on 04/Apr/21 $(- 1) \times \frac{1}{π . i} = ?$ Answered by Engr_Jidda last updated on 04/Apr/21 $(- 1) \times \frac{1}{π i} = i^{2} \frac{1}{π i} = \frac{i}{π}$ Terms of…

What-is-the-remainder-13-163-when-divided-by-99-

Tinku Tara June 3, 2023 Number Theory 0 Comments

Question Number 137383 by bramlexs22 last updated on 02/Apr/21 $W h a t i s t h e r e m a i n d e r 13^{163} w h e n$ $d i v i d e d b y 99$ Answered by EDWIN88 last updated on 02/Apr/21 $By Euler Theorem$ $$\varphi\left(\mathrm{99}\right)\:=\:\mathrm{3}\left(\mathrm{3}−\mathrm{1}\right)\left(\mathrm{11}−\mathrm{1}\right)=\:\mathrm{60}\:…

Find-the-remainder-7-30-divide-by-10-

Tinku Tara June 3, 2023 Number Theory 0 Comments

Question Number 137364 by liberty last updated on 02/Apr/21 $F i n d t h e r e m a i n d e r 7^{30} d i v i d e$ $b y 10$ Answered by MJS_new last updated on 02/Apr/21 $$\mathrm{7}^{\mathrm{0}} =\mathrm{1} \…

52-9-48-31-27-13-65-

Tinku Tara June 3, 2023 Number Theory 0 Comments

Question Number 6280 by prakash jain last updated on 21/Jun/16 $52 : 9 :: 48 : 31 :: 27 : 13 :: 65 : ?$ Commented by prakash jain last updated on 21/Jun/16 $The question from a mental ability test .$ Answered…

Question-71806

Tinku Tara June 3, 2023 Number Theory 0 Comments

Question Number 71806 by ahmadshahhimat775@gmail.com last updated on 20/Oct/19 Answered by MJS last updated on 20/Oct/19 ${(- 2)}^{\sqrt{2}} = {({2 e}^{i π})}^{\sqrt{2}} = 2^{\sqrt{2}} e^{i π \sqrt{2}} =$ $$=\mathrm{2}^{\sqrt{\mathrm{2}}} \mathrm{cos}\:\pi\sqrt{\mathrm{2}}\:+\mathrm{2}^{\sqrt{\mathrm{2}}}…

Category: Number Theory