Question

Gasiti si scoateti un factor comun cand calculati urmatoarele sume:
8+16+24+32+...+4000
11+22+33+44+...+7700

Answer 1

$\displaystyle a).8+16+24+32+...+4000=8(1+2+3+4+...+500)= \\ \\ =8 \times \frac{500(500+1)}{2} =8 \times \frac{500 \times 501}{2} =8 \times \frac{250500}{2} = \\ \\ =8 \times 125250=1002000 \\ \\ b).11+22+33+44+...+7700=11(1+2+3+...+700)= \\ \\ =11 \times \frac{700(700+1)}{2} =11 \times \frac{700 \times 701}{2} =11 \times \frac{490700}{2} = \\ \\ =11 \times 245350=2698850$