Chứng minh : $\frac{1}{2^{2}} + \frac{1}{3^{2}} + \frac{1}{4^{2}} + .... + \frac{1}{100^{2}} < 1$
Edited by Mikhail Leptchinski, 21-12-2014 - 13:46.
$\frac{1}{2^{2}} + \frac{1}{3^{2}} + \frac{1}{4^{2}} + .... + \frac{1}{100^{2}} < 1$
Started By minhhien2001, 20-12-2014 - 16:19
#2
Posted 20-12-2014 - 16:40
JayVuTF
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$Chứng minh : \frac{1}{2^{2}} + \frac{1}{3^{2}} + \frac{1}{4^{2}} + .... + \frac{1}{100^{2}} < 1$
$ta có \frac{1}{n^2}<\frac{1}{n(n-1)}=\frac{1}{n}-\frac{1}{n-1}$
$\Rightarrow \frac{1}{2^{2}} + \frac{1}{3^{2}} + \frac{1}{4^{2}} + .... + \frac{1}{100^{2}} < 1-\frac{1}{2}+\frac{1}{2}+\frac{1}{3}-\frac{1}{3}+....+\frac{1}{99}-\frac{1}{100} <1$
$\Rightarrow dpcm$
Edited by JayVuTF, 20-12-2014 - 17:02.
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