Question

suma 2/3*5+2/5*7+2/7*9......+2/31*33=

Answer 1

$S=\frac{2}{3*5}+ \frac{2}{5*7}+ \frac{2}{7*9}+...+\frac{2}{31*33} \\\\\\ \frac{2}{3*5}=\frac{1}{3}-\not \frac{1}{5} \\\\ \frac{2}{5*7}=\not \frac{1}{5}- \not \frac{1}{7} \\ .\\.\\. \\\\ \frac{2}{31*33}=\not \frac{1}{31} -\frac{1}{33} \\\\\\ \hbox{Se simplifica pe diagonala nr. pozitive cu cele negative si se obtine:} \\\\ S=\frac{1}{3}^{(11}-\frac{1}{33}= \frac{11-1}{33} \\\\\\ \boxed{S=\frac{10}{33} }$