Question Number 106240 by pticantor last updated on 03/Aug/20
$$ \\ $$$$ \\ $$$$ \\ $$$$\boldsymbol{{li}}\underset{\boldsymbol{{n}}\rightarrow+\infty} {\boldsymbol{{m}}}\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\frac{\left(−\mathrm{1}\right)^{\boldsymbol{{k}}+\mathrm{1}} }{\boldsymbol{{k}}}=???? \\ $$
Answered by Dwaipayan Shikari last updated on 03/Aug/20
$$\mathrm{1}−\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{3}}−\frac{\mathrm{1}}{\mathrm{4}}+\frac{\mathrm{1}}{\mathrm{5}}−\frac{\mathrm{1}}{\mathrm{6}}+....={log}\left(\mathrm{1}+\mathrm{1}\right)={log}\left(\mathrm{2}\right) \\ $$
Commented by Ari last updated on 05/Aug/20
but how so? could you explain please!