Question Number 138560 by Raxreedoroid last updated on 14/Apr/21 $$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\left(−\mathrm{1}\right)^{{n}} \left(\mathrm{ln}\:\left({n}+\mathrm{1}\right)−\mathrm{ln}\:\left({n}\right)\right)=? \\ $$ Answered by Dwaipayan Shikari last updated on 14/Apr/21 $$\underset{{n}=\mathrm{1}} {\overset{\infty}…
Question Number 7449 by Tawakalitu. last updated on 29/Aug/16 $${The}\:{sum}\:{of}\:{the}\:{first}\:\mathrm{3}\:{terms}\:{of}\:{an}\:{AP}\:{is}\:\mathrm{36}\:{and}\:{the} \\ $$$${product}\:{of}\:{the}\:{first}\:\mathrm{3}\:{terms}\:{of}\:{a}\:{GP}\:{is}\:\mathrm{1728}.\:{if}\:{the} \\ $$$${second}\:{term}\:{of}\:{the}\:{linear}\:{sequence}\:{is}\:\mathrm{12}\:{and}\:{such} \\ $$$${that}\:{the}\:{second}\:{term}\:{of}\:{the}\:{GP}\:{is}\:{equal}\:{to}\:{the}\:{second} \\ $$$${term}\:{of}\:{the}\:{AP}.\:{find} \\ $$$$\left(\mathrm{1}\right)\:{The}\:{AP} \\ $$$$\left(\mathrm{2}\right)\:{The}\:{GP} \\ $$ Answered…
Question Number 138513 by mathlove last updated on 14/Apr/21 Answered by MJS_new last updated on 14/Apr/21 $${AB}+\mathrm{9}=\mathrm{3}\left({BA}\right) \\ $$$$\mathrm{10}{A}+{B}+\mathrm{9}=\mathrm{30}{B}+\mathrm{3}{A} \\ $$$${A}=\frac{\mathrm{29}{B}−\mathrm{9}}{\mathrm{7}}\:\Rightarrow\:{B}=\mathrm{2}\wedge{A}=\mathrm{7} \\ $$$$\mathrm{72}+\mathrm{9}=\mathrm{3}×\mathrm{27} \\ $$$${A}+{B}=\mathrm{9}…
Question Number 7442 by lakshaysethi last updated on 29/Aug/16 $${is}\:\mathrm{0}×\mathrm{0}\:{not}\:{defined}\:{or}\:{equal}\:{to}\:\mathrm{0}? \\ $$$${if}\:{it}\:{is}\:{not}\:{defined}\:{then}\:{why}? \\ $$ Commented by Rasheed Soomro last updated on 29/Aug/16 $$\mathrm{0}×\mathrm{0}\:{is}\:{defined}\:{and}\:{it}\:{is}\:{equal}\:{to}\:\mathrm{0}. \\ $$…
Question Number 138511 by mathlove last updated on 14/Apr/21 Commented by MJS_new last updated on 14/Apr/21 $$\mathrm{005}\:\:\:\:\:\mathrm{014}\:\:\:\:\:\mathrm{023}\:\:\:\:\:\mathrm{113}\:\:\:\:\:\mathrm{122}\:\:\:\:\:… \\ $$$$\mathrm{050}\:\:\:\:\:\mathrm{140}\:\:\:\:\:\mathrm{230}\:\:\:\:\:\mathrm{131}\:\:\:\:\:\mathrm{221} \\ $$$$\mathrm{500}\:\:\:\:\:\mathrm{401}\:\:\:\:\:\mathrm{302}\:\:\:\:\:\mathrm{311}\:\:\:\:\:\mathrm{212} \\ $$$$==\:\:\:\:\:==\:\:\:\:\:==\:\:\:\:\:==\:\:\:\:\:== \\ $$$$\mathrm{555}\:\:\:\:\:\mathrm{555}\:\:\:\:\:\mathrm{555}\:\:\:\:\:\mathrm{555}\:\:\:\:\:\mathrm{555}…
Question Number 72965 by Raxreedoroid last updated on 05/Nov/19 $$\mathrm{Prove}\:\mathrm{that}\:\mathrm{this}\:\mathrm{equation}\:\mathrm{is}\:\mathrm{true}: \\ $$$$\underset{{x}=\mathrm{1}} {\overset{{n}−\mathrm{1}} {\prod}}\left(\mathrm{2}{x}+\mathrm{1}\right)=\frac{\left(\mathrm{2}{x}−\mathrm{1}\right)!}{\left(\mathrm{2}\right)^{{x}−\mathrm{1}} \left({x}−\mathrm{1}\right)!} \\ $$ Commented by mathmax by abdo last updated on…
Question Number 7399 by Tawakalitu. last updated on 27/Aug/16 $${In}\:{an}\:{AP}\:,\:{if}\:{the}\:{m}^{{th}} \:{term}\:{is}\:{n}\:{and}\:{the}\:{n}^{{th}} \:{term} \\ $$$${is}\:{m}.\:{where}\:{m}\:{is}\:{not}\:{equal}\:{to}\:{n}.\:{find} \\ $$$$\left(\mathrm{1}\right)\:{The}\:{value}\:{of}\:\left({m}\:+\:{n}\right)^{{th}} \:{term} \\ $$$$\left(\mathrm{2}\right)\:{The}\:{p}^{{th}} \:{term}. \\ $$ Answered by Yozzia…
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Question Number 7263 by Tawakalitu. last updated on 19/Aug/16 Commented by Rasheed Soomro last updated on 20/Aug/16 $${I}\:{have}\:{answered}\:{your}\:{question}#\mathrm{6852} \\ $$$${which}\:{is}\:{very}\:{resembling}\:{to}\:{this}\:{question}. \\ $$$${Please}\:{see}\:{if}\:{you}\:{have}\:{not}\:{seen}\:{yet}. \\ $$ Commented…