Question

Ma puteti ajuta? Ofer coroana daca este corect

Answer 1

3/2*5+3/5*8+3/8*11+....+3/2012*2015=
=1/2-1/5+1/5-1/8+1/8-1/11+....+1/2012-1/2015=
=1/2-1/2015=(2015-2)/2*2015=2013/4030

Answer 2

$\displaystyle \frac{3}{2 \cdot 5} + \frac{3}{5 \cdot 8} + \frac{3}{8 \cdot 11} +...+ \frac{3}{2012 \cdot 1015} = \\ \\ = \frac{1}{2} - \frac{1}{5} + \frac{1}{5} - \frac{1}{8} + \frac{1}{8} - \frac{1}{11} +...+ \frac{1}{2012} - \frac{1}{2015} = \\ \\ = \frac{1}{2} - \frac{1}{2015} = \frac{2015-2}{4030} = \frac{2013}{4030}$