find-the-function-represented-by-the-series-m12xmmdisplaystylesumm1inftyfrac2xmm

Question

Find the function represented by the series ∑m=1∞(2x)mm\displaystyle{\sum_{m=1}^{\infty}}\frac{(2x)^m}{m} .

Accepted Answer

−ln⁡(1−2x)-\ln(1-2x)[−12,12)\left\lbrack-\frac{1}{2},\frac{1}{2}\right)

Answer

−ln⁡(1−2x)-\ln(1-2x) [−12,12]\left\lbrack-\frac{1}{2},\frac{1}{2}\right\rbrack

Answer

−ln⁡(1−2x)-\ln(1-2x) (−12,12)\left(-\frac{1}{2},\frac{1}{2}\right)

Answer

−ln⁡(1−4x)-\ln(1-4x)[−12,12)\left\lbrack-\frac{1}{2},\frac{1}{2}\right)

Find the function represented by the series ∑m=1∞(2x)mm\(\displaystyle{\sum_{m=1}\)^{\(\infty\)}}\(\frac{(2x)^m}{m}\) .