Question

Calculati: a) 1+2+3+3+...+29 b) 10+20+30+...+200 c) 5+10+15+20+...+125 d) 19+20+21+22+...+39 Prin metoda sumei gauss​

Answer 1

Răspuns:

Explicație pas cu pas:

a) 1+2+3+3+...+29 = (1+29)·29:2 = 29·15= 435

b) 10+20+30+...+200 = 10·(1+2+3+...+20) = 10·(1+20)·20:2 =

= 10·21·10 = 2100

10+20+30+...+200 = (10+200)·[(200-10):10+1]:2 =

= 210·20:2 = 210·10 = 2100

c) 5+10+15+20+...+125 = 5·(1+2+3+...+25) = 5·(1+25)·25:2 =

= 125·13 = 1625

5+10+15+20+...+125 = (5+125)·[(125-5):5+1]:2 =

= 130·25:2 = 65·25 = 1625

d) 19+20+21+22+...+39 = (19+39)·(39-19+1):2 =

= 58·21:2 = 29·21 = 609

Formula lui Gauss :

Sₙ = (a₁+aₙ)·[(aₙ-a₁):r +1]:2

a₁ = primul termen

aₙ = ultimul termen

r = ratia = (a₂-a₁)

(aₙ-a₁):r +1 = numarul de termeni