Category: Arithmetic

Question Number 57770 by Tawa1 last updated on 11/Apr/19 Answered by Kunal12588 last updated on 11/Apr/19 $$\underset{k=1}{\sum ^{13}}\frac{1}{sin(\frac{\pi }{4}+\frac{(k-1)\pi }{6})sin(\frac{\pi }{4}+\frac{k\pi }{6})}$$$$sin(\frac{\pi }{4}+\frac{(k-1)\pi }{6})sin(\frac{\pi }{4}+\frac{k\pi }{6})$$$$=sin\left(\frac{3\pi +2(k-1)\pi }{12}\right)sin\left(\frac{3\pi +2k\pi }{12}\right)$$$$={sin}\left(\frac{\left(\mathrm{2}{k}+\mathrm{1}\right)\pi}{\mathrm{12}}\right){sin}\left(\frac{\left(\mathrm{2}{k}+\mathrm{3}\right)\pi}{\mathrm{12}}\right)…

Question Number 188796 by Rupesh123 last updated on 07/Mar/23 Commented by mr W last updated on 07/Mar/23 $$consideryourquestion:$$$$f\left(n\right)shouldbedivisiblebyn.but$$$$theexamplesyougavearenot$$$${fibonacci}\:{series}\:{and}\:{are}\:{not}\:{divisible} \…

Question Number 188564 by BaliramKumar last updated on 03/Mar/23 $$1\times 2+2\times 3+3\times 4+\dots \dots \dots \dots \dots +24\times 25=?$$ Answered by universe last updated on 03/Mar/23 $$\left(\mathrm{1}^{\mathrm{2}} +\mathrm{1}\right)+\left(\mathrm{2}^{\mathrm{2}} +\mathrm{2}\right)+\left(\mathrm{3}^{\mathrm{2}} +\mathrm{3}\right)+……\left(\mathrm{24}^{\mathrm{2}} +\mathrm{24}\right) \…

Question Number 188456 by Rupesh123 last updated on 01/Mar/23 Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 188442 by BaliramKumar last updated on 03/Mar/23 $$$$$$Solvebycomputerprograming$$$$\left(ifpossible\right)d<a<b\mathrm{\&}c<a,b>2c$$$$\cancel{a^2+b^2=5c^2+2d^2}(a,b,c,d\in \mathrm{N})$$$${c}^{\mathrm{2}} +{d}^{\mathrm{2}} \:=\:{a}^{\mathrm{2}} \:\:\:\:\:\:\:\:………\left({i}\right)…