Question

S=1+3+5+7+......+125
S=2+4+6+8+......+2000

Answer 1

Răspuns:

Explicație pas cu pas:

S=1+3+5+7+......+125 = 1+2+3+....+125+126 - 2-4-6...-126 =

126*127/2 - 2*63*64/2 = 63*127 - 63*64 = 63*(127-64) = 63*63

S=2+4+6+8+......+2000 = 2 * (1+2+3+...+1000) = 2 * 1000*1001/2 = 1000*1001

Answer 2

1 + 3 + .. + 2n - 1 = n²

2n - 1 = 125 => 2n = 126 => n = 63

1 + 3 + .. + 125 = 63² = 3969

2 + 4 + .. + 2000 =

= 2(1 + 2 + .. + 1000)

= 2×1000×1001 : 2

= 1000×1001

= 1001000