Question

1x2 + 2x3 +3x4 +.........+99x100

lâu ngày k làm quên gùichỉ mìn nha

Answer 1

Đặt \(A=1.2+2.3+3.4+...+99.100\)

\(\Rightarrow3A=1.2.3+2.3.\left(4-1\right)+...+99.100.\left(101-98\right)\)

\(\Rightarrow3A=1.2.3+2.3.4-1.2.3+...+99.100.101-98.99.100\)

\(\Rightarrow3A=99.100.101\)

\(\Rightarrow A=99.100.101:3\)

\(\Rightarrow A=33.100.101\)

\(\Rightarrow A=333300\)

Answer 2

Ai được tick nhớ ơn tui nha

Answer 3

thui mìn bít làm ùi

Answer 4

đặt 1x2 +2x3+3x4+..........+99x100 =A

A3 = 1x2 x3 +2x3 x3+.....+99x100x3

A3= 1x2x3 + 2x3x(4-1) + 3x4x(5-2)
+........+99x100x(101-98)

A3=1x2x3+2x3x4-1x2x3-2x3x4+....
+99x100x101-98x99x100

A3=99x100x101

A3=111110

A=3333000

Answer 5

đặt 1x2 +2x3+3x4+..........+99x100 =A

A3 = 1x2 x3 +2x3 x3+.....+99x100x3

A3= 1x2x3 + 2x3x(4-1) + 3x4x(5-2)
+........+99x100x(101-98)

A3=1x2x3+2x3x4-1x2x3-2x3x4+....
+99x100x101-98x99x100

A3=99x100x101

A3=111110

A=3333000

Answer 6

đặt 1x2 +2x3+3x4+..........+99x100 =A

A3 = 1x2 x3 +2x3 x3+.....+99x100x3

A3= 1x2x3 + 2x3x(4-1) + 3x4x(5-2)
+........+99x100x(101-98)

A3=1x2x3+2x3x4-1x2x3-2x3x4+....
+99x100x101-98x99x100

A3=99x100x101

A3=111110

A=3333000

Answer 7

đặt 1x2 +2x3+3x4+..........+99x100 =A

A3 = 1x2 x3 +2x3 x3+.....+99x100x3

A3= 1x2x3 + 2x3x(4-1) + 3x4x(5-2)
+........+99x100x(101-98)

A3=1x2x3+2x3x4-1x2x3-2x3x4+....
+99x100x101-98x99x100

A3=99x100x101

A3=111110

A=3333000

Answer 8

đặt 1x2 +2x3+3x4+..........+99x100 =A

A3 = 1x2 x3 +2x3 x3+.....+99x100x3

A3= 1x2x3 + 2x3x(4-1) + 3x4x(5-2)
+........+99x100x(101-98)

A3=1x2x3+2x3x4-1x2x3-2x3x4+....
+99x100x101-98x99x100

A3=99x100x101

A3=111110

A=3333000

Answer 9

Gọi biểu thức trên là A, ta có :

A = 1x2 + 2x3 + 3x4 + 4x5 + ...+ 99x100

A x 3 = 1x2x3 + 2x3x3 + 3x4x3 + 4x5x3 + ... + 99x100x3

A x 3 = 1x2x3 + 2x3x(4-1) + 3x4x(5-2) + 4x5x(6-3) + ... + 99x100x(101-98)

A x 3 = 1x2x3 + 2x3x4 - 1x2x3 + 3x4x5 - 2x3x4 + 4x5x6 - 3x4x5 + ... + 99x100x101 - 98x99x100.

A x 3 = 99x100x101

A = 99x100x101 : 3

A = 333300