Question

Calculează:
a) 11 + 12 + ... + 18 + 19;
b) 111 +222 + ... + 999;
c) 200 + 205 + 210 + ... + 300;
d) 101 + 103 + 105 + ... + 199. Dau coroana ​

Answer 1

Răspuns:

Explicație pas cu pas:

a) 11 + 12 + ...+ 18 + 19 = 9*(11 + 19)/2 = 9*30/2 = 9*15 = 135

____________

b)

111 + 222 + ...+ 999 = 111*(1 + 2 + ...+ 9) = 111*9*(1 + 9)/2 = 111*9*10/2 = 4995

_____________

c)

200 + 205 + 210 + ....+ 300 = 21*(200 + 300)/2 = 21*500/2 = 5250

_____________

d)

101 + 103 + 105 + ...+ 199 = 50*(101 + 199)/2 = 50*300/2 = 7500

199 = 101 + (n - 1)*2 = 101 + 2n - 2 = 99 + 2n

2n = 199 - 99 = 100

n = 50 termeni in suma