# It is a question of limit. Please find the answer and send me. I am very thankful for the help.

abhishek
39 Points
2 years ago
As you can see it is 0/0 form of indetermency.
Hence apply l hopitals stepwise
Look at below$\lim _{x \rightarrow 0} \frac{1}{x}\left[n^{2}-\left(\frac{1}{1^{x}}+\frac{1}{2^{x}}+\cdots \cdots+\frac{1}{n x}\right)^{2}\right] \frac{0}{0} form : Apply L- tiopital Pube \lim _{x \rightarrow 0}\left(0-2\left(\frac{1}{1^{x}}+\frac{1}{2^{x}}+\cdots+\frac{1}{n^{x}}\right) \cdot\left(1^{-x}(-1) \ln 1+2^{-x}(-1) \ln 2\right.\right. \left.n^{-x}(-1) \ln n\right) \Rightarrow 2 n \cdot \ln (n !) \Rightarrow \ln(n))^{2 n}$