Ta có: 3S = 1.2.(3-0) + 2.3.(4-1) + 3.4.(5-2)  + .....+ 50.51.(52 -49) 

              = 1.2.3 - 0  + 2.3.4 - 1.2.3 + 3.4.5 -2.3.4 + .....+ 50.51.52 - 49.50.51

 3S = 50.51.52

  S = 50.17.52 =44200

3S = 1.2.(3-0) + 2.3.(4-1) + 3.4.(5-2)  + .....+ 50.51.(52 -49) 

    = 1.2.3 - 0  + 2.3.4 - 1.2.3 + 3.4.5 -2.3.4 + .....+ 50.51.52 - 49.50.51

 3S = 50.51.52

S = 50.17.52 =44200

 A=1.2+2.3+3.4+...+49.50+50.51

3A= 1.2.3+2.3.3+3.4.3+...+49.50.3+50.51.3

3A= 1.2.(3-0)+2.3.(4-1)+3.4.(5-2)+...+49.50.(51-48)+50.51.(52-49)

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 + 49.50.51 - 50.51.52

3A= 50.51.52

3A=132600

  A=66300

vay tu di ma tinh

Đặt A = 1.2 + 2.3 + 3.4 + ... + 50.51

=> 3A = 1.2.3 + 2.3.3 + 3.4.3 + ... + 50.51.3

=> 3A = 1.2.3 + 2.3.(4 - 1) + 3.4.(5 - 2) + ... + 50.51.(52 - 49)

=> 3A = 1.2.3 + 2.3.4 - 1.2.3 + 3.4.5 - 2.3.4 + ... + 50.51.52 - 49.50.51

=> 3A = 50.51.52

=> A = 50.17.52

=> A = 44200

Vậy 1.2 + 2.3 + 3.4 + ... + 50.51 = 44200

A=2(1-3)+4(5-3)+ 6(5-7)+...+50(49-57)

A=-4-8-12-...-100 = -(4+8+12+...+100) (tính tổng cấp số cộng)

Ta có:A=\(\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+......+\dfrac{1}{49.50}+\dfrac{1}{50.51}\)

A=\(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+.......+\dfrac{1}{49}-\dfrac{1}{50}+\dfrac{1}{50}-\dfrac{1}{51}\)

A=1-\(\dfrac{1}{51}=\dfrac{50}{51}\)

\(A=\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+...+\dfrac{1}{49.50}+\dfrac{1}{50.51}\)

\(A=\dfrac{1}{1}-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{49}-\dfrac{1}{50}+\dfrac{1}{50}-\dfrac{1}{51}\)

\(A=\dfrac{1}{1}-\dfrac{1}{51}\)

\(A=\dfrac{50}{51}\)

A = \(\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+...+\dfrac{1}{49.50}+\dfrac{1}{50.51}\)

= \(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{49}-\dfrac{1}{50}+\dfrac{1}{50}-\dfrac{1}{51}\)

= \(1-\dfrac{1}{51}\)

= \(\dfrac{50}{51}\)

A = \(\dfrac{1}{1.2}\) + \(\dfrac{1}{2.3}\)+ \(\dfrac{1}{3.2}\)+ ....+ \(\dfrac{1}{50.51}\)

A = \(\dfrac{1}{1}\) - \(\dfrac{1}{2}\)+ \(\dfrac{1}{2}\) - \(\dfrac{1}{3}\) + \(\dfrac{1}{3}\) - \(\dfrac{1}{2}\)+...+ \(\dfrac{1}{50}\) - \(\dfrac{1}{51}\)

A = \(\dfrac{1}{1}\) - \(\dfrac{1}{51}\)

A = \(\dfrac{50}{51}\)

Kp = 50/51

A = 1 /1.2 + 1/ 2.3 + 1 /3.4 + . . . + 1/ 49.50 + 1/ 50.51

 A = 2 − 1/ 1.2 + 3 − 2 /2.3 + 4 − 3 /3.4 + . . . + 50 − 49 /49.50 + 51 − 50/ 50.51

A = 1 − 1/ 2 + 1/ 2 − 1 /3 + 1 /3 − 1/ 4 + . . . + 1 /50 − 1 /51

A=1-1/51

A=50/51

Cảm ơn bn

B=6/4.7+6/7.10+6/10.13+...+6/73.76

=2.(3/4.7 +3/7.10 +3/10.13 +...+3/73.76 )

=2.(1/4 −1/7 +1/7 −1/10 +1/10 −1/13 +...+1/73 −1/76 )

=2.(1/4-1/76)=2.9/38=9/19