Question

Demonstrati ca $\frac {1}{ √1}+ \frac {1}{ √2}+ \frac {1}{ √3}+...+ \frac {1}{ √9999}>99,99.$

Answer 1

Notez suma cu S.

$\frac{1}{ \sqrt{1} } > \frac{1}{ \sqrt{10000} } = \frac{1}{100}=0,01$
$\frac{1}{ \sqrt{2} } > \frac{1}{ \sqrt{10000} } = \frac{1}{100}=0,01$
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$\frac{1}{ \sqrt{9999} } > \frac{1}{ \sqrt{10000}} = \frac{1}{100}=0,01$
Aduni relatiile...
Si obtii: S>0,01*9999=99,99.