Find the limit, interpreting it as a limit of a summation of a suitably chosen function:
$$\lim_{n\to\infty} n \bigg( \frac{1}{n^{2} + 1^{2}} + \frac{1}{n^{2} + 2^{2}} + ... + \frac{1}{n^{2} + n^{2}} \bigg).$$
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7See http://math.stackexchange.com/questions/1399008/using-right-hand-riemann-sum-to-evaluate-the-limit-of-fracnn21-cdots?rq=1 – Robert Z Nov 09 '16 at 09:12
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http://math.stackexchange.com/questions/465075/find-lim-limits-n-to-infty-frac1n-sum-limits2n-r-1-fracr-sq – lab bhattacharjee Nov 09 '16 at 09:24
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We have $n*\frac{1}{n^2+k^2}=\frac{1}{n}*\frac{1}{1+(\frac{k}{n})^2}$.
Loook at $f(x)=\frac{1}{1+x^2}$
Fred
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