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Category: Algebra

1-9-1-18-1-30-1-45-1-63-1-84-

Question Number 200931 by Spillover last updated on 26/Nov/23 $$\frac{\mathrm{1}}{\mathrm{9}}+\frac{\mathrm{1}}{\mathrm{18}}+\frac{\mathrm{1}}{\mathrm{30}}+\frac{\mathrm{1}}{\mathrm{45}}+\frac{\mathrm{1}}{\mathrm{63}}+\frac{\mathrm{1}}{\mathrm{84}}+…\infty=? \\ $$$$ \\ $$ Answered by MM42 last updated on 26/Nov/23 $${s}_{{n}} =\frac{\mathrm{2}}{\mathrm{3}}\left(\frac{\mathrm{1}}{\left({n}+\mathrm{1}\right)\left({n}+\mathrm{2}\right)}\right)=\frac{\mathrm{2}}{\mathrm{3}}\left(\frac{\mathrm{1}}{{n}+\mathrm{1}}−\frac{\mathrm{1}}{{n}+\mathrm{2}}\right)\:\: \\ $$$$\Rightarrow{s}_{{n}}…

lim-x-sin1-1-x-2-1-cosx-

Question Number 200795 by mathlove last updated on 23/Nov/23 $$\underset{{x}\rightarrow{sin}\mathrm{1}} {\mathrm{lim}}\:\frac{\mathrm{1}−{x}^{\mathrm{2}} }{\mathrm{1}+{cosx}}=? \\ $$ Answered by witcher3 last updated on 23/Nov/23 $$\mathrm{x}\rightarrow\frac{\mathrm{1}−\mathrm{x}^{\mathrm{2}} }{\mathrm{1}+\mathrm{cos}\left(\mathrm{x}\right)}\:\mathrm{is}\:\:\mathrm{defined}\:\mathrm{in}\:\mathrm{sin}\left(\mathrm{1}\right) \\ $$$$…

sinx-cosx-tgx-x-

Question Number 200788 by hardmath last updated on 23/Nov/23 $$\mathrm{sin}\boldsymbol{\mathrm{x}}\:\:\:+\:\:\:\mathrm{cos}\boldsymbol{\mathrm{x}}\:\:\:=\:\:\:\mathrm{tg}\boldsymbol{\mathrm{x}} \\ $$$$\mathrm{x}\:=\:? \\ $$ Answered by Frix last updated on 23/Nov/23 $${x}=\mathrm{2tan}^{−\mathrm{1}} \:{t}\:\mathrm{leads}\:\mathrm{to} \\ $$$${t}^{\mathrm{4}}…