Tuesday, 16 October 2018

Series, computing the limit limlimitsntoinftyfrac1+2+cdots+nn3




How to compute the following limit? The series is given by



lim



Thanks for your help...


Answer



Just for fun:



\lim_{n\rightarrow\infty}\frac{1}{n}\left(\frac{1}{n}\frac{1}{n}+\frac{2}{n}\frac{1}{n}+\ldots+\frac{n}{n}\frac{1}{n}\right)=\lim_{n\rightarrow\infty}\frac{1}{n}\times\int_{0}^{1}\text{d}x=0


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