Compute the sum of the series $\sum_{n=1}^{\infty} \frac{1}{n \cdot 2^n}$ [duplicate]
What would be the sum of the following series?
$$\sum_{n=1}^{\infty} \frac{1}{n \cdot 2^n}$$
Thanks
Solution 1:
$$\ln(1-x)=-\sum_{n=1}^\infty\frac{x^n}n$$
Can you recognize $x$ here?
See also: Taylor series for $\log(1+x)$ and its convergence