Oblicz granice ciagu

[MIKE21]

Mam zadanie z którym nie moge sobie poradzić:

\(\displaystyle{ \lim_{n\to } [ \frac{1}{n} + \frac{1}{n+1} + \frac{1}{n+2} + \frac{1}{n+3} + ... + \frac{1}{n+n} ]}\)

Z góry dziękuje za pomoc!

[natkoza]

\(\displaystyle{ =\lim_{n\to\infty} \frac{(n^{2}+2)(n+1)}{2n}=\lim_{n\to\infty} \frac{n^{3}+n^{2}+2n+2}{2n}=\lim_{n\to\infty} \frac{n^{3}(1+\frac{1}{n}+\frac{2}{n^{2}}+\frac{2}{n^{3}})}{2n}=\lim_{n\to\infty} \frac{n^{2}}{2}=\infty}\)

[Sir George]

natkoza, a od kiedy to \(\displaystyle{ \frac1n+\frac1{n+1}+\ldots+\frac1{2n}\ \overbrace{\ =\ }^{\Large ???} \ \frac{(n^2+2)(n+1)}{2n}}\)