Category: Algebra

Question Number 158465 by HongKing last updated on 04/Nov/21 Answered by qaz last updated on 04/Nov/21 $$\underset{\mathrm{n}=0}{\sum ^{\mathrm{\infty }}}\frac{\left(\begin{array}{c}2\mathrm{n}\\ \mathrm{n}\end{array}\right)}{4^{\mathrm{n}}(4\mathrm{n}+5)(2\mathrm{n}+2)}$$$$=\frac{\mathrm{1}}{\mathrm{2}}\underset{\mathrm{n}=\mathrm{0}} {\overset{\infty} {\sum}}$$\left(\begin{array}{c}-1/2\\ \mathrm{n}\end{array}\right)$$\left(−\mathrm{1}\right)^{\mathrm{n}} \left(\frac{\mathrm{1}}{\mathrm{n}+\mathrm{1}}−\frac{\mathrm{4}}{\mathrm{4n}+\mathrm{5}}\right)…

Question Number 27382 by abdo imad last updated on 05/Jan/18 $$resolveinsideC{\left(\frac{z-i}{z+i}\right)}^n+{\left(\frac{z+i}{z-i}\right)}^n=2cos\theta and0<\theta <\pi .ninteger.$$ Answered by sma3l2996 last updated on 05/Jan/18 $$\left(\frac{{z}−{i}}{{z}+{i}}\right)^{{n}} +\left(\frac{{z}−{i}}{{z}+{i}}\right)^{−{n}} −\mathrm{2}{cos}\theta=\mathrm{0}…

Question Number 27376 by macanudo last updated on 05/Jan/18 Commented by prakash jain last updated on 05/Jan/18 $$\mathrm{S}=\underset{k=0}{\sum ^{2n}}{(-1)}^k{x}^k$$$${S}=\mathrm{1}−{x}+{x}^{\mathrm{2}} −{x}^{\mathrm{3}} +{x}^{\mathrm{4}}…

Question Number 158443 by HongKing last updated on 04/Nov/21 $$\mathrm{How}\mathrm{many}\mathrm{divisors}\mathrm{has}\mathrm{the}\mathrm{positive}$$$$\mathrm{integer}\mathbf{n}\mathrm{which}\mathrm{verify}$$$${\mathrm{n}}^{\mathbf{n}}={2027}^{{2027}^{2028}}?$$ Answered by MJS_new last updated on…

Question Number 92899 by gonzo last updated on 09/May/20 $$y=-2.241x+1.585$$$$howdoifindvalueofxbyrearranging$$ Commented by mr W last updated on 09/May/20 $$x=\frac{1.585-y}{2.241}$$…