Question

[super saiyan blue]

Tính tổng S= 1.2+2.3+3.4+...+99.100

Answer 1

[soyeon_Tiểu bàng giải]

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

3S = 1.2.(3-0) + 2.3.(4-1) + 3.4.(5-2) + ... + 99.100.(101-98)

3S = 1.2.3 - 0.1.2 + 2.3.4 - 1.2.3 + 3.4.5 - 2.3.4 + ... + 99.100.101 - 98.99.100

3S = 99.100.101

S = 33.100.101

S = 333 300

Ủng hộ mk nha ^_-

Answer 2

[Nguyễn Việt Hoàng]

Ta có: S = 1.2 + 2.3 + 3.4 + ... + 99.100

=> 3S = 1.2.(3-0) + 2.3.(4-1) + 3.4.(5-2) + ... + 99.100.(101-98)

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

=> 3S = 98.99.100

=> S = \(\frac{98.99.100}{3}=333300\)