Question

1x2+2x3+.........x99+100

 

Answer 1

#)Giải :

Đặt \(A=1.2+2.3+3.4+...+99.100\)

\(3A=1.2.3+2.3.3+3.4.3+...+49.50.3\)

\(3A=1.2.\left(3-0\right)+2.3.\left(4-1\right)+3.4.\left(5-2\right)+...+49.50.\left(51-48\right)\)

\(3A=0.1.2-1.2.3+1.2.3-2.3.4+2.3.4-3.4.5+...+48.49.50-49.50.51\)

\(3A=49.50.51=124950\)

\(\Leftrightarrow A=\frac{124950}{3}=41650\)

Answer 2

Mình sửa lại đề vì sai :  1 x 2 + 2 x 3 + ... + 99 x 100

Đặt A = 1 x 2 + 2 x 3 + ... + 99 x 100

  => 3 x A = 3 x (1 x 2 + 2 x 3 + ... + 99 x 100)

  => 3 x A = 1 x 2 x 3 + 2 x 3 x 3 + ... + 99 x 100 x 3

  => 3 x A = 1 x 2 x 3 + 2 x 3 x (4 - 1) + ... + 99 x 100 x (101 - 98)

  => 3 x A = 1 x 2 x 3 + 2 x 3 x 4 - 1 x 2 x 3 + ... + 99 x 100 x 101 - 98 x 99 x 100

  => 3 x A = 99 x 100 x 101

  => 3 x A = 999 900

  => A       = 999 900 : 3

  => A       = 333 300

Vậy 1 x 2 + 2 x 3 + ... + 99 x 100 = 333 300

Answer 3

A = 1.2 + 2.3 + 3.4 + ... + 99.100

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

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

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

3A = 99.100.101

A = 99.100.101 : 3 = 333300

Answer 4

T = 1 x 2 + 2 x 3 + ... + 99 x 100

3T = 1 x 2 x 3 + 2 x 3 x (4 - 1) + ... + 99 x 100 x (101 - 98)

3T = 1 x 2 x 3 + 2 x 3 x 4 - 1 x 2 x 3 + 3 x 4 x 5 - 2 x 3 x 4 + ... + 99 x 100 x 101 - 98 x 99 x 100

3T = 99 x 100 x 101

\(\Rightarrow\)T = 99 x 100 x 101 : 3 

\(\Rightarrow\)T = 333300

Answer 5

Đặt C = 1x2+2x3+.........x99+100

\(\Rightarrow3C=1.2.3+2.3.3+..+99.100.3\)3

\(\Rightarrow3C=1.2.3+2.3.\left(4-1\right)+...+99.100.\left(101-98\right)\)

\(\Rightarrow\)\(3C=1.2.3+2.3.4-1.2.3+...+99.100.101-98.99.100\)

\(\Rightarrow3C=98.99.100\)\(\Rightarrow C=\frac{98.99.100}{3}\)\(=333300\)