Question

Efectuati;
a) 1supra 55+2 supra55+3supra 55+...+10supra 55
Ma poate ajuta cineva la suma lui Gauss

Answer 1

$\displaystyle \frac{1}{55} + \frac{2}{55} + \frac{3}{55} +...+ \frac{10}{55} =1+2+3+...+10= \\ \\ = \frac{10(10+1)}{2} = \frac{10 \cdot 11}{2}= \frac{110}{2} =55 \Leftrightarrow \\ \\ \Leftrightarrow \frac{1}{55} + \frac{2}{55} + \frac{3}{55} +...+ \frac{10}{55} = \frac{55}{55} =\boxed{1}$