Question Number 3650 by prakash jain last updated on 18/Dec/15 $$\mathrm{If}\:{a}_{{n}} \:\mathrm{is}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{all}\:\mathrm{primitive}\:{n}^{{th}} \:\mathrm{root}\:\mathrm{of} \\ $$$$\mathrm{unity}. \\ $$$$\mathrm{Does}\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}{a}_{{n}} \:\mathrm{converge}? \\ $$$$\mathrm{An}\:{n}^{{th}} \:\mathrm{root}\:\mathrm{of}\:\mathrm{unity},\:\mathrm{say}\:{z},\:\mathrm{is}\:\mathrm{primitive}\:\mathrm{if}\:\mathrm{it}\:\mathrm{is}\:\mathrm{not} \\ $$$${k}^{{th}}…
Question Number 69176 by MASANJAJ last updated on 21/Sep/19 $${difference}\:{of}\:{two}\:{complementary}\: \\ $$$${angles}\:{is}\:\mathrm{102}^{°} .{find}\:{two}\:{angles} \\ $$ Commented by mr W last updated on 21/Sep/19 $${you}\:{mean}\:{two}\:{supplementary}\:{angles}? \\…
Question Number 69162 by Learner-123 last updated on 20/Sep/19 $${Find}\:{the}\:{local}\:{extreme}\:{values}\:{of} \\ $$$${the}\:{function}\:: \\ $$$${f}\left({x},{y}\right)=\:{xy}−{x}^{\mathrm{2}} −{y}^{\mathrm{2}} −\mathrm{2}{x}−\mathrm{2}{y}+\mathrm{4}. \\ $$ Answered by MJS last updated on 20/Sep/19…
Question Number 3617 by Rasheed Soomro last updated on 16/Dec/15 $${If}\:\:{the}\:{G}.{M}.\:{between}\:{two}\:{numbers}\: \\ $$$${a}\:,\:{b}\:\:\:{is}\:\:{G}\:{and}\:{the}\:{two}\:{A}.{M}.'{s}\:{between} \\ $$$${them}\:{are}\:{p}\:\:{and}\:\:{q}\:,\:{then}\:{prove}\:{that} \\ $$$${G}^{\mathrm{2}} =\left(\mathrm{2}{p}−{q}\right)\left(\mathrm{2}{q}−{p}\right). \\ $$ Commented by Yozzii last updated…
Question Number 3615 by Rasheed Soomro last updated on 16/Dec/15 $${Find}\:{the}\:{value}\:{of}\:{n}\:{so}\:{that} \\ $$$$\frac{{a}^{{n}+\mathrm{1}} +{b}^{{n}+\mathrm{1}} }{{a}^{{n}} +{b}^{{n}} } \\ $$$${may}\:{become}\:{the}\:{H}.{M}.\:{between} \\ $$$${a}\:\:\:{and}\:\:\:\:{b}. \\ $$ Commented by…
Question Number 69143 by ajfour last updated on 20/Sep/19 $${x}^{\mathrm{4}} +{ax}^{\mathrm{3}} +{bx}^{\mathrm{2}} +{cx}+{d}=\mathrm{0} \\ $$$${let}\:\:{x}={f}\left({t}\right)\:\:{linear}\:{perhaps} \\ $$$${t}^{\mathrm{4}} +{At}^{\mathrm{3}} +{Bt}^{\mathrm{2}} +{Ct}+{D}=\mathrm{0} \\ $$$${can}\:{we}\:{have}\:\: \\ $$$$\:\:\:\mathrm{4}{AB}={A}^{\mathrm{3}} +\mathrm{8}{C}\:\:{solving}\:{at}\:{most}…
Question Number 134668 by EDWIN88 last updated on 06/Mar/21 $$\mathrm{1}+\mathrm{1}+\mathrm{4}−\mathrm{6}−\mathrm{8}−\mathrm{10}+\mathrm{12}+\mathrm{14}+\mathrm{16}−\mathrm{18}−\mathrm{20}−\mathrm{22}+… \\ $$$$\mathrm{S}_{\mathrm{900}} \:=\:? \\ $$ Answered by benjo_mathlover last updated on 06/Mar/21 $$\Rightarrow\underset{\mathrm{6}} {\underbrace{\mathrm{1}+\mathrm{1}+\mathrm{4}}}\:\underset{−\mathrm{24}} {\underbrace{−\mathrm{6}−\mathrm{8}−\mathrm{10}}}\:\underset{\mathrm{42}}…
Question Number 3588 by prakash jain last updated on 16/Dec/15 $$\mathrm{Three}\:\mathrm{point}\:\mathrm{are}\:\mathrm{drawn}\:\mathrm{on}\:\mathrm{a}\:\mathrm{straight} \\ $$$$\mathrm{number}\:\mathrm{line}\:\mathrm{A},\mathrm{B}\:\mathrm{and}\:\mathrm{C}. \\ $$$$\mathrm{Consider}\:\mathrm{a}\:\mathrm{quadractic}\:\mathrm{equation} \\ $$$${x}^{\mathrm{2}} +{ax}+{b}=\mathrm{0} \\ $$$${a}=\mathrm{Length}\:\mathrm{of}\:\mathrm{line}\:\mathrm{segment}\:\mathrm{AB} \\ $$$${b}=\mathrm{Length}\:\mathrm{of}\:\mathrm{line}\:\mathrm{segment}\:\mathrm{BC} \\ $$$$\mathrm{Give}\:\mathrm{construction}\:\mathrm{steps}\:\mathrm{to}\:\mathrm{identify}\:\mathrm{a}\:\mathrm{points} \\…
Question Number 3565 by Yozzii last updated on 15/Dec/15 $${Define}\:{the}\:{sequence}\:\left\{{a}_{{n}} \right\}\:{by}\:{the} \\ $$$${recurrence}\:{equation}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{a}_{{n}+\mathrm{1}} ={pa}_{{n}} +{qa}_{{n}−\mathrm{1}} \:\:\left({n}\geqslant\mathrm{1}\right) \\ $$$${where}\:{p},{q}\in\mathbb{C}−\left\{\mathrm{0}\right\}\:{and}\: \\ $$$${a}_{\mathrm{0}} =\alpha\:,\:{a}_{\mathrm{1}} =\beta\:\: \\…
Question Number 3564 by Yozzii last updated on 15/Dec/15 $${Test}\:{for}\:{convergence}: \\ $$$$\left(\mathrm{1}\right)\:\underset{{n}=\mathrm{10}} {\overset{\infty} {\sum}}\frac{\mathrm{2}^{\mathrm{ln}\left(\mathrm{ln}{n}\right)} }{{n}\mathrm{ln}{n}} \\ $$$$\left(\mathrm{2}\right)\underset{{n}=\mathrm{2}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{{n}\left(\mathrm{ln}{n}\right)^{\mathrm{p}} }\:\left(\mathrm{two}\:\mathrm{cases}\:\mathrm{of}\:\mathrm{p}\:\mathrm{to}\:\mathrm{look}\:\mathrm{at}\right) \\ $$$$\left(\mathrm{3}\right)\underset{{n}=\mathrm{2}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{{n}} \sqrt{{n}}}{\mathrm{ln}{n}}…