Question and Answers Forum

All Questions      Topic List

None Questions

Previous in All Question      Next in All Question      

Previous in None      Next in None      

Question Number 212646 by MrGaster last updated on 20/Oct/24

$$$$$$\underset{n\to \mathrm{\infty }}{\lim }\underset{i=1}{\sum ^n}\underset{j=i}{\sum ^i}\frac{i(i+j)}{(n^2+i^2)(n^2+j^2)}$$

Commented by mr W last updated on 21/Oct/24

$$\underset{j=1}{\sum ^i}.....$$

Answered by MrGaster last updated on 31/Oct/24

$$\underset{n\to \mathrm{\infty }}{\lim }\underset{i=1}{\sum ^n}\frac{2i^2}{{(n^2+i^2)}^2}$$$$\underset{n\to \mathrm{\infty }}{\lim }\frac{1}{n}\underset{i=1}{\sum ^n}\frac{2{\left(\frac{i}{n}\right)}^2}{(1+{\left(\frac{i}{n}\right)}^2)}\cdot \frac{1}{n}$$$${\int }_0^1\frac{2x^2}{{(1+x^2)}^2}dx$$$${[-\frac{x}{1+x^2}+\arctan \left(x\right)]}_0^1$$$$-\frac{1}{2}+\frac{\pi }{4}$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com