Tìm $lim(x_{n})$ với $x_{n}=\frac{1}{n+1}+\frac{1}{n+2}+...+\frac{1}{n+n}$
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Posted 15-11-2014 - 07:39
PRONOOBCHICKENHANDSOME
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$ \lim_{n \to \infty} x_n = \lim_{n \to \infty} \sum_{k=1}^n \frac{1}{n+k} = \lim_{n \to \infty} \frac{1}{n} \sum_{k=1}^n \frac{1}{1+\frac{k}{n}} = \int_0^1 \frac{dx}{1+x} = \ln 2 $
Edited by PRONOOBCHICKENHANDSOME, 15-11-2014 - 07:41.
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