Question

Calculati folosind formula lui garuss:
a)1+2+3+.....+200
b)1+2+3+4+.....+1999
c)1+2+3+4+.....+2000

Answer 1

200(200+1):2=100*201=20100 1999(1999+1):2=999.5*2000 =1999000 2000(2000+1):2=1000*2001 =2001000

Answer 2

$\displaystyle a).1+2+3+...+200= \frac{200(200+1)}{2} = \frac{200 \times 201}{2} = \frac{40200}{2} =20100 \\ \\ b).1+2+3+4+...+1999= \frac{1999(1999+1)}{2} = \frac{1999 \times 2000}{2} = \\ \\ = \frac{3998000}{2} =1999000 \\ \\ c).1+2+3+4+...+2000= \frac{2000(2000+1)}{2} = \frac{2000 \times 2001}{2} = \\ \\ = \frac{4002000}{2} =2001000$