Question

Sum to n terms of the series $logm+log\frac{m^2}{n}+log\frac{m^3}{n^2}+log\frac{m^4}{n^3}\dots \dots$ is

• A. $log{\left(\frac{m^{n+1}}{n^{n-1}}\right)}^{\frac{n}{2}}$
• B. $log{\left(\frac{n^{n-1}}{m^{n+1}}\right)}^{\frac{n}{2}}$
• C. $log{\left(\frac{m^n}{n^n}\right)}^{\frac{n}{2}}$
• D. $log{\left(\frac{m^{1-n}}{n^{1-m}}\right)}^{\frac{n}{2}}$

Answer 1

The correct option is A $log{\left(\frac{m^{n+1}}{n^{n-1}}\right)}^{\frac{n}{2}}$

$log(m\times m^2\times m^3\times .........m^n)-log(1\times n\times n^2\times ......n^{(n-1)})=log{\left[\frac{m^{(n+1)}}{n^{(n-1)}}\right]}^{\left(n/2\right)}$