Question

31. Calculați: a) 1+2+3+4+...+29; c) 5+10+15+20+...+125; b) 10+20+30+...+200 d) 19+20+21+22+...+39.
prin metoda gauss​

Answer 1

a) 1 + 2 + 3 + 4 + ... + 29 =

(29 x 30) : 2 =  

870 : 2 = 435

b) 10 + 20 + 30 +.. .+ 200 = | : 10

S = 1 + 2 + 3 + ... +20

10S = 10 x  [(20 x 21) : 2] =

10S = 10 x 210 = 2100

c) 5 + 10 + 15 + 20 + ... + 125 = | : 5

S = 1 + 2 + 3 + 4 + ... +25 =

5S = 5 x [(26 x 25) : 2]

5S = 5 x 325

5S = 1625

d) 19 + 20 + 21 + 22 + ... + 39 =

39-19+1=21 (termeni)

21 x (19 + 39) : 2=21 x 29=609