Show that the sum of the infinite series
$$ \log{2}\mathrm{e}-\log{4}\mathrm{e}+\log{16}\mathrm{e}-\ldots+(-1)^{n}\log{2^{2^{n}}}\mathrm{e}+\ldots $$ is $$ \frac{1}{\ln(2\sqrt{2})} $$
[ $\log_{a}b=c$ is equivalent to $a^{c}=b$ ]
Math 01
· One min read
Student