Đặt \(A=1.4+2.5+3.6+...+100.103\)

\(=1\left(2.2\right)+2\left(3+2\right)+3\left(4+2\right)+...+100\left(101+2\right)\)

\(=1.2+2.3+3.4+...+100.101+\left(1.2+2.2+3.2+...+100.2\right)\)

\(=1.2+2.3+3.4+...+100.101+2\left(1+2+3+...+100\right)\)

\(=1.2+2.3+3.4+...+100.101+2.100\left(100+1\right):2\)

\(=1.2+2.3+3.4+...+100.101+10100\)

Đặt \(B=1.2+2.3+3.4+...+100.101\)

\(\Rightarrow3B=1.2.3+2.3.3+3.4.3+100.101.3\)

\(\Rightarrow3B=1.2.3+2.3\left(4-1\right)+3.4\left(5-2\right)+...+100.101\left(102-99\right)\)

\(\Rightarrow3B=1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+...+100.101.102-99.100.101\)

\(\Rightarrow3B=100.101.102\)

\(\Rightarrow B=343400\)

Khi đó \(A=343400=10100=333300\)

Đặt A = 1.4 + 2.5 + 3.6 + 4.7 + ... + 100.103

3A = 3.(1.2 + 2.3 + 3.4 + ... + 100.101] + 3.(2 + 4 + 6 + ... + 200)

     = 1.2.3 + 2.3.3 + 3.4.3 + ... + 100.101.3 + 3.(2 + 4 + 6 + ... + 200)

\(\Rightarrow\) A  =  100.101.105:3 = 353500

Đặt A = 1.4 + 2.5 + 3.6 + ... + 100.103

= 1.(2 + 2) + 2.(3 + 2) + 3.(4 + 2) +.... + 100.(101 + 2)

= 1.2 + 2.3 + 3.4 + ... + 100.101 + (1.2 + 2.2 + 3.2 + ... + 100.2)

= 1.2 + 2.3 + 3.4 + ... + 100.101 + 2(1 + 2 + 3 + .... + 100)

= 1.2 + 2.3 + 3.4 + .... + 100.101 + 2.100.(100 + 1) : 2

= 1.2 + 2.3 + 3.4 + ... + 100.101 + 10100

Đặt B = 1.2 + 2.3 + 3.4 + .... + 100.101

=> 3B = 1.2.3 + 2.3.3 + 3.4.3 + .... + 100.101.3

=> 3B = 1.2.3 + 2.3.(4 - 1) + 3.4.(5 - 2) + ... + 100.101.(102 - 99)

=> 3B = 1.2.3 + 2.3.4 - 1.2.3 + 3.4.5 - 2.3.4 + .... + 100.101.102 - 99.100.101

=> 3B = 100.101.102

=> B = 343400

Khi đó A = 343400 - 10100 = 333300

bạn tính kiểu khác đc ko ? kiểu ab mình ko hiểu lắm

Ta thấy: 1.4 = 1.(1 + 3)

2.5 = 2.(2 + 3)

3.6 = 3.(3 + 3)

4.7 = 4.(4 + 3)

…….

n(n + 3) = n(n + 1) + 2n

Vậy C = 1.2 + 2.1 + 2.3 + 2.2 + 3.4 + 2.3 + … + n(n + 1) +2n

C = 1.2 + 2 +2.3 + 4 + 3.4 + 6 + … + n(n + 1) + 2n

C = [1.2 +2.3 +3.4 + … + n(n + 1)] + (2 + 4 + 6 + … + 2n)

⇒ 3C = 3.[1.2 +2.3 +3.4 + … + n(n + 1)] + 3.(2 + 4 + 6 + … + 2n) 

3C = 1.2.3 + 2.3.3 + 3.4.3 + … + n(n + 1).3 + 3.(2 + 4 + 6 + … + 2n)

3C = n(n + 1)(n + 2) + 

⇒ C =  +  = 

Ta thấy: 1.4 = 1.(1 + 3)

2.5 = 2.(2 + 3)

3.6 = 3.(3 + 3)

4.7 = 4.(4 + 3)

…….

n(n + 3) = n(n + 1) + 2n

Vậy C = 1.2 + 2.1 + 2.3 + 2.2 + 3.4 + 2.3 + … + n(n + 1) +2n

C = 1.2 + 2 +2.3 + 4 + 3.4 + 6 + … + n(n + 1) + 2n

C = [1.2 +2.3 +3.4 + … + n(n + 1)] + (2 + 4 + 6 + … + 2n)

⇒ 3C = 3.[1.2 +2.3 +3.4 + … + n(n + 1)] + 3.(2 + 4 + 6 + … + 2n) 

3C = 1.2.3 + 2.3.3 + 3.4.3 + … + n(n + 1).3 + 3.(2 + 4 + 6 + … + 2n)

3C = n(n + 1)(n + 2) + 

⇒ C =  +  = 

Ta thấy: 1.4 = 1.(1 + 3)

2.5 = 2.(2 + 3)

3.6 = 3.(3 + 3)

4.7 = 4.(4 + 3)

…….

n(n + 3) = n(n + 1) + 2n

Vậy C = 1.2 + 2.1 + 2.3 + 2.2 + 3.4 + 2.3 + … + n(n + 1) +2n

C = 1.2 + 2 +2.3 + 4 + 3.4 + 6 + … + n(n + 1) + 2n

C = [1.2 +2.3 +3.4 + … + n(n + 1)] + (2 + 4 + 6 + … + 2n)

⇒ 3C = 3.[1.2 +2.3 +3.4 + … + n(n + 1)] + 3.(2 + 4 + 6 + … + 2n) 

3C = 1.2.3 + 2.3.3 + 3.4.3 + … + n(n + 1).3 + 3.(2 + 4 + 6 + … + 2n)

3C = n(n + 1)(n + 2) + 

⇒ C =  +  = 

Đề có thiếu ko vậy bạn

Tính nhanh:

2 . 31 . 12 + 4 . 6 . 42 + 8 . 27 . 3