Question

Calculati:
a) 2+4+6+....+50
b) 2+4+6+...+100
c) 2+4+6+....+500
d) 2+4+6+...+1000

Answer 1

$\displaystyle a).2+4+6+...+50=2(1+2+3+...+25)= \\ \\ =2 \cdot \frac{25(25+1)}{2} =2 \cdot \frac{25 \cdot 26}{2} =2 \cdot \frac{650}{2} =2 \cdot 325=650 \\ \\ b).2+4+6+...+100=2(1+2+3+...+50)= \\ \\ =2 \cdot \frac{50(50+1)}{2} =2 \cdot \frac{50 \cdot 51}{2} =2 \cdot \frac{2550}{2} =2 \cdot 1275=2550 \\ \\ c).2+4+6+...+500=2(1+2+3+...+250)= \\ \\ =2 \cdot \frac{250(250+1)}{2} =2 \cdot \frac{250 \cdot 251}{2} =2 \cdot \frac{62750}{2} =2 \cdot 31375=62750$

$\displaystyle d).2+4+6+...+1000=2(1+2+3+...+500)= \\ \\ =2 \cdot \frac{500(500+1)}{2} =2 \cdot \frac{500 \cdot 501}{2} =2 \cdot \frac{250500}{2} =2 \cdot 125250=250500$