Question

Arătaţi că 1 supra 10 x 11 + 1 supra 11 x 12 + ... + 1 supra 99 x 100 > 0.08 .

Answer 1

$\frac{1}{10*11} + \frac{1}{11*12}+....+ \frac{1}{99*100} > 0.08 \\ \\ \frac{1}{10} - \frac{1}{11} + \frac{1}{11} - \frac{1}{12} +.....+ \frac{1}{99} - \frac{1}{100} > 0.08 \\ \\ \frac{1}{10} - \frac{1}{100} >0.08 \\ \\ \frac{10}{100} - \frac{1}{100} > 0.08 \\ \\ \frac{9}{100} >0.08 \\ \\ 0.09>0.08$