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Author: Tinku Tara

lim-n-0-k-1-n-k-2-3k-2-k-2-2k-1-1-n-

Question Number 212618 by MrGaster last updated on 19/Oct/24 $$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\underset{{n}\rightarrow\mathrm{0}} {\mathrm{lim}}\left(\underset{{k}=\mathrm{1}} {\overset{{n}} {\prod}}\frac{{k}^{\mathrm{2}} +\mathrm{3}{k}+\mathrm{2}}{{k}^{\mathrm{2}} +\mathrm{2}{k}+\mathrm{1}}\right)^{\frac{\mathrm{1}}{{n}}} \\ $$ Commented by mehdee7396 last updated on…

Verify-the-equation-tan-nx-k-1-n-1-2-1-k-1-n-2k-1-tan-2k-1-x-k-0-n-2-1-k-n-2k-tan-2k-x-

Question Number 212615 by MrGaster last updated on 19/Oct/24 $$\mathrm{Verify}\:\mathrm{the}\:\mathrm{equation}:\mathrm{tan}\:{nx}=\underset{{k}=\mathrm{1}} {\overset{\left[\frac{{n}+\mathrm{1}}{\mathrm{2}}\right]} {\sum}}\left(−\mathrm{1}\right)^{{k}−\mathrm{1}} \begin{pmatrix}{{n}}\\{\mathrm{2}{k}−\mathrm{1}}\end{pmatrix}\:\mathrm{tan}^{\mathrm{2}{k}−\mathrm{1}} {x}/\underset{{k}=\mathrm{0}} {\overset{\left[\frac{{n}}{\mathrm{2}}\right]} {\sum}}\left(−\mathrm{1}\right)^{{k}} \begin{pmatrix}{{n}}\\{\mathrm{2}{k}}\end{pmatrix}\mathrm{tan}^{\mathrm{2}{k}} {x} \\ $$ Terms of Service Privacy Policy…

Help-me-to-solve-pls-Q-212576-

Question Number 212598 by MATHEMATICSAM last updated on 18/Oct/24 $$\mathrm{Help}\:\mathrm{me}\:\mathrm{to}\:\mathrm{solve}\:\mathrm{pls} \\ $$$$\mathrm{Q}\:\mathrm{212576}\: \\ $$ Answered by A5T last updated on 18/Oct/24 $${Lemma}:\:\frac{{a}}{{b}}=\frac{{c}}{{d}}\Rightarrow\frac{{a}}{{b}}=\frac{{c}}{{d}}=\frac{{a}\underset{−} {+}{c}}{{b}\underset{−} {+}{d}} \\…

lim-n-1-2-n-2-1-2-2-n-2-2-3-2-n-2-3-n-2-n-2-n-n-3-

Question Number 212595 by MrGaster last updated on 18/Oct/24 $$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\left(\frac{\mathrm{1}^{\mathrm{2}} }{{n}^{\mathrm{2}} +\mathrm{1}}+\frac{\mathrm{2}^{\mathrm{2}} }{{n}^{\mathrm{2}} +\mathrm{2}}+\frac{\mathrm{3}^{\mathrm{2}} }{{n}^{\mathrm{2}} +\mathrm{3}}+\ldots+\frac{{n}^{\mathrm{2}} }{{n}^{\mathrm{2}} +{n}}−\frac{{n}}{\mathrm{3}}\right)=? \\ $$ Answered by Berbere last…