Question

Calculati:
5+10+15+20+25+....+1000

Answer 1

Factor comun 5 si avem:
5(1+2+3+........+200)

La paranteze folosm suma lui Gauss si avem :
1+2+3+........+200= [(1+200)*200]/2=201*200/2=201*100=20100

Deci toata sums S= 5* 20100=100500

Answer 2

$\displaystyle 5+10+15+20+25+...+1000=5(1+2+3+...+200)= \\ \\ =5 \times \frac{200(200+1)}{2} =5 \times \frac{200 \times 201}{2} =5 \times \frac{40200}{2} = \\ \\ =5 \times 20100=100500$