Question Number 136098 by SOMEDAVONG last updated on 18/Mar/21 $$\left.\mathrm{I}\right).\mathrm{compute}\:\underset{\mathrm{k}=\mathrm{0}} {\overset{\mathrm{1000}} {\sum}}\mathrm{C}_{\mathrm{2000}} ^{\mathrm{2k}} . \\ $$ Answered by Olaf last updated on 18/Mar/21 $$\left(\mathrm{1}−\mathrm{1}\right)^{\mathrm{2000}} \:=\:\mathrm{0}\:=\:\underset{{p}=\mathrm{0}}…
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Question Number 5011 by Yozzii last updated on 01/Apr/16 Commented by Yozzii last updated on 01/Apr/16 $${S}=\underset{{n}\rightarrow\infty} {\mathrm{lim}}\left(\frac{\mathrm{1}}{{ln}\left({n}\right)}\underset{{i}=\mathrm{1}} {\overset{{n}} {\sum}}\frac{{tan}^{−\mathrm{1}} {i}}{{n}−{i}+\mathrm{1}}\right) \\ $$$${S}=?\: \\ $$…
Question Number 5003 by 314159 last updated on 30/Mar/16 $${Find}\:{the}\:{coefficient}\:{of}\:{x}^{\mathrm{17}} \:{in}\:{the}\:{expansion}\:{of} \\ $$$$\left({x}+\mathrm{1}\right)\left({x}+\mathrm{2}\right)\left({x}+\mathrm{3}\right)…\left({x}+\mathrm{19}\right). \\ $$ Commented by 123456 last updated on 30/Mar/16 $$\mathrm{1}+\mathrm{1}+…+\mathrm{1}\:\left(\mathrm{17}\right) \\ $$$$\mathrm{1}+\mathrm{1}+…+\mathrm{1}\:\left(\mathrm{17}\right)+\mathrm{0}…
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Question Number 70513 by naka3546 last updated on 05/Oct/19 Commented by naka3546 last updated on 05/Oct/19 $${x}\:=\:? \\ $$$${y}\:=\:? \\ $$$${without}\:\:{trigonometry}\:. \\ $$ Terms of…
Question Number 136040 by zakirullah last updated on 18/Mar/21 $$\:\:\:\:\:\:{find}\:{the}\:{smallest}\:{number}\:{which}\:{when}\:{we}\:{divide}\:{by}\:\mathrm{12},\mathrm{15},\mathrm{18},\:\mathrm{and}\:\mathrm{27}\:\mathrm{leaves}\:\mathrm{a}\:\mathrm{remainder} \\ $$$$\:\:\:\:\:\:\mathrm{of}\:\mathrm{8},\mathrm{11},\mathrm{14}\:\mathrm{and}\:\mathrm{23}\:\mathrm{respectively}? \\ $$ Answered by mr W last updated on 18/Mar/21 $${N}=\mathrm{27}{a}+\mathrm{23}=\mathrm{27}{a}+\mathrm{9}+\mathrm{14} \\ $$$$\mathrm{27}{a}+\mathrm{9}=\mathrm{18}{b}\:\Rightarrow\mathrm{3}{a}+\mathrm{1}=\mathrm{2}{b}\:\Rightarrow{a}=\mathrm{2}{c}+\mathrm{1}…
Question Number 70499 by Sayantan chakraborty last updated on 04/Oct/19 Commented by Tinku Tara last updated on 05/Oct/19 $$\mathrm{Hi}\:\mathrm{Sayantan} \\ $$$$\mathrm{Ability}\:\mathrm{to}\:\mathrm{draw}\:\mathrm{shapes}\:\mathrm{is}\:\mathrm{a}\:\mathrm{reaonable} \\ $$$$\mathrm{and}\:\mathrm{we}\:\mathrm{will}\:\mathrm{work}\:\mathrm{on}\:\mathrm{it}. \\ $$$$\mathrm{We}\:\mathrm{gave}\:\mathrm{out}\:\mathrm{work}\:\mathrm{for}\:\mathrm{third}\:\mathrm{party}\:\mathrm{for}…
Question Number 4954 by Dnilka228 last updated on 26/Mar/16 $$ \\ $$$$ \\ $$ Commented by Dnilka228 last updated on 26/Mar/16 $$\sqrt{\boldsymbol{\mathrm{e}}^{\mathrm{2}_{\boldsymbol{\rho}} } }×\frac{\mathrm{1}}{\mathrm{4}}+{f}^{+{n}} −{f}\left({n}\right)…
Question Number 4953 by PEACE007 last updated on 26/Mar/16 $${how}\:{to}\:{change}\:{language} \\ $$ Commented by Tinku Tara last updated on 26/Mar/16 $$\mathrm{Currently}\:\mathrm{only}\:\mathrm{roman}\:\mathrm{alphabets}\:\mathrm{are}\:\mathrm{present}. \\ $$$$\mathrm{Which}\:\mathrm{language}\:\mathrm{do}\:\mathrm{you}\:\mathrm{want}.\:\mathrm{We}\:\mathrm{will} \\ $$$$\mathrm{consider}\:\mathrm{adding}\:\mathrm{it}\:\mathrm{in}\:\mathrm{future}\:\mathrm{update}.…