What seems is not actually............

Calculus Level 5

Find the value of $\displaystyle \lim_{n \to \infty} \ln \left(e^n\left(\dfrac {n}{n+1}\right)^{n^2}\right)$

1 solution

Tanishq Varshney
Jan 31, 2015

use log(ab)=loga +logb

Put $n=\frac{1}{x}$

$\displaystyle \lim_{x \to 0} \frac{1}{x}(\frac{1}{x} ln(\frac{1}{1+x})+1)$

= $\displaystyle \lim_{x\to 0}\frac{1}{x}(1-\frac{1}{x}ln(1+x))$

= $\displaystyle \lim_{x\to 0}\frac{x-(x-\frac{x^{2}}{2}+\frac{x^{3}}{3}-...)}{x^{2}}$

= $\frac{1}{2}$

plz do upvote

Is this mcalurin series for log x

Tejas Suresh - 5 years, 11 months ago