Question Number 10186 by prakash jain last updated on 29/Jan/17
![Prove ln (1+(1/n))^n =[1−(1/(2(n+1)))+(1/(2∙3(n+1)^2 ))−(1/(3∙4(n+1)^3 ))+..]](https://www.tinkutara.com/question/Q10186.png)
$$\mathrm{Prove} \\ $$$$\mathrm{ln}\:\left(\mathrm{1}+\frac{\mathrm{1}}{{n}}\right)^{{n}} =\left[\mathrm{1}−\frac{\mathrm{1}}{\mathrm{2}\left({n}+\mathrm{1}\right)}+\frac{\mathrm{1}}{\mathrm{2}\centerdot\mathrm{3}\left({n}+\mathrm{1}\right)^{\mathrm{2}} }−\frac{\mathrm{1}}{\mathrm{3}\centerdot\mathrm{4}\left({n}+\mathrm{1}\right)^{\mathrm{3}} }+..\right] \\ $$