## Calculus 8th Edition

$ln(1+\frac{3}{5})$ or $ln(8)-ln(5)$
Given: $\Sigma_{n=0}^{\infty}{(-1)^{n-1}}\dfrac{3^{n}}{5^{n}(n)}$ $=\Sigma_{n=0}^{\infty}{(-1)^{n-1}}\dfrac{3^{n}(1/5^{n})}{n}$ $=\Sigma_{n=0}^{\infty}{(-1)^{n-1}}\dfrac{(\frac{3}{5})^{n}}{n}$ As we know $ln(1+x)=\Sigma_{n=0}^{\infty}{(-1)^{n-1}}\dfrac{x^{n}}{n}$ Thus, $ln(1+\frac{3}{5})=\Sigma_{n=0}^{\infty}{(-1)^{n-1}}\dfrac{(\frac{3}{5})^{n}}{n}$ or $ln(1+\frac{3}{5})=ln(\frac{8}{5})=ln(8)-ln(5)$ Hence, $ln(1+\frac{3}{5})$ or $ln(8)-ln(5)$