Question

Aratati ca 1/10*11+1/11*12+...+1/99*100>0,08

Answer 1

1/10 - 1/11 + 1/11 - 1/12 + 1/12 + 1/13 +........+1/99 - 1/100 = 1/10 - 1/100 = 9/100  = 0,09 > 0,08.

Answer 2

$\displaystyle \frac{1}{10 \cdot 11} + \frac{1}{11 \cdot 12} +...+ \frac{1}{99\cdot 100} = \\ \\ = \frac{1}{10} - \frac{1}{11} + \frac{1}{11} - \frac{1}{12} +...+ \frac{1}{99} - \frac{1}{100} = \\ \\ = \frac{1}{10} - \frac{1}{100} = \frac{10-1}{100} = \frac{9}{100} \ \textgreater \ 0,08$