Question

Tinh
1^2+2^2+...+99^2
tim x
(x-3)+(x-2)+...+10+11

1 cau =1 tick

 

Answer 1

1^2 + 2^2 + 3^2 + ... + 99^2

= 1(2 - 1) + 2(3 - 1) + 3(4- 1) + ... + 98(99-1) + 99(100 -1)

= 1.2 -1.1 + 2.3 - 2.1 + 3.4 - 3.1 + ... + 98.99 + 98.1 + 99.100 - 99

= (1.2 + 2.3 + 3.4 + ... + 99.100) - (1 + 2 + 3 + ... + 99)

đặt S = 1.2 + 2.3 + 3.4 + ... + 99.100

3S = 1.2.3 + 2.3.3 + 3.4.3 + ... + 99.100.3

3S = 1.2.3 + 2.3.(4 - 1) + 3.4.(5 - 2) + .... + 99.100.(101 - 98)

3S = 1.2.3 + 2.3.4 - 1.2.3 + 3.4.5 - 2.3.4 + ... + 99.100.101 - 98.99.100

3S = 99.100.101

S = 99.100.101 : 3 = 333300

A = 1 + 2 + 3 + ... + 99

A = (99 + 1).99 : 2 = 4950

Tinh ra là :

333300 - 4950 = 328350