Question

Tính tổng

S=1.2+2.3+3.4+4.5+.....+98.99+99.100

Các bạn giúp mình với mình cảm ơn rất nhiều

Chiều nay mình phải nộp bài mong các bạn giúp mình với

Answer 1

Đặt S= 1.2 + 2.3 + 3.4 + ...+ 99.100
3S = 1.2.3+2.3.3+3.4.3+...+98.99.3+99.100.3
3S= 1.2.3+2.3(4-1)+3.4(5-2)+...+98.99(100-97)+99.100(101-98)
3S= 1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+...-97.98.99+99.100.101-98.99.100
3S = 99.100.101\(\ge\) 3S = 3.33.100.101
S=33.100.101= 333300

Answer 2

S = 1.2 + 2.3 + 3.4 + 4.5 + ... + 98.99 + 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 + ... + 99.100.101 - 98.99.100
=> 3S = 99.100.101
=> 3S = 3.33.100.101
=> S = 33.100.101 = 333300
@Nguyen Tran Ngoc Diep

Answer 3

S=1.2+2.3+3.4+3.4+.....+98.99+99.100

3S=1.2.3+2.3.3+3.4.3+4.5.3+...+98.99.3+99.100.3

3S=1.2.(3-0)+2.3(4-1)+3.4.(5-2)+...+98.99.(100-97)+99.100.(101-98)

3S=1.2.3-0.1.2+2.3.4-1.2.3+3.4.5-2.3.4+...+98.99.100+97.98.99+99.100.101-98.99.100

3S=99.100.101

S=\(\dfrac{\text{99.100.101}}{3}=33.100.101=333300\)

Answer 4

Ta có : \(S=1.2+2.3+3.4+4.5+...+98.99+99.100\)

\(3S=1.2.3+2.3.3+3.4.3+...+99.100.3\)

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

\(3S=1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+...-97.98.99+99.100.101-98-99.100\)

\(3S=99.100.101\ge3S=3.33.100.101\)

\(S=33.100.101=333300\)