The value of limn→∞ ∑$$K=1n$$ $$Kn2+K2$$

Question

The value of  limn→∞ ∑$$K=1n$$ $$Kn2+K2$$

Infinity Learn · Accepted Answer

limn→∞∑$$k=1n$$ $$Kn2+K2=limn$$→∞∑$$k=1n$$ $$Kn2+K2$$                                      $$=limn$$→∞∑$$k=1n$$ $$1n2$$×$$K1+Kn2$$                                     $$=limn$$→∞∑$$k=1n$$ $$1n$$×$$K/n1+Kn2$$                                     $$=$$∫$$01x1+x2dx$$                                     $$=12log1+x201$$                                    $$=12log2$$

$The value of lim_{n \to \infty} \sum_{K = 1}^{n} \frac{K}{n^{2} + K^{2}}$

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The value of limn→∞ ∑K=1n Kn2+K2

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$The value of lim_{n \to \infty} \sum_{K = 1}^{n} \frac{K}{n^{2} + K^{2}}$