Question

Calculati
$\frac{17}{42} + \frac{18}{42} +\frac{19}{42} +...+ \frac{84}{42}$

Answer 1

17/42+18/42+19/42+...+84/42 =
$\frac{17+18+19+...+84}{42}=\\ =\frac{(1+2+...16)+17+18+...+84 \;-\;(1+2+3+...+16)}{42}=\\ =\frac{84*85:2\;-\;16*17:2}{42}=\\ =\frac{3570-136}{42}=\\ =\frac{3434}{42}=\frac{1717}{21}$