Вычислите: 1)1+2+3+...+50 2)11+12+13+...+60 3) 1+3+5+...+99 4)3+6+9...+90 Пример: 1+2+3+...+98+99+100= 101*50=5050

1) 1+2+3+...+50.

n=50, a1 = 1, a50 = 50.

Sn = (a1 + an) * n / 2.

S50 = (1 + 50) * 50 / 2 = 51* 50 / 2 = 1275.

2)11+12+13+...+60.

an = 60, a1 = 11, d=1.

an = a1 + d(n - 1).

60 = 11 + n -1.

n = 50.

S50 = (11 + 60) * 50 / 2 = 71 * 50 / 2 = 1775.

3) 1+3+5+...+99.

an = 99, a1 = 1, d = 2.

99 = 1 + 2 * (n - 1).

99 = 1 + 2n - 2.

2n = 100.

n = 50.

S50 = (1 + 99) * 50 / 2 = 100 * 50 / 2 = 2500.

4)3+6+9...+90.

an = 90, a1 = 3, d = 3.

90 = 3 + 3 * (n - 1).

90 = 3 + 3n - 3.

3n = 90.

n = 30.

S30 = (3 + 90) * 30 / 2 = 93 * 30 / 2 = 1395.