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)

=43.61

Lời giải:

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

$=(1.2.3+2.3.4+3.4.5+...+50.51.52)-(0.1.2+1.2.3+2.3.4+....+49.50.51)$

$=50.51.52$

$\Rightarrow A=50.51.52:3=44200$

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

Sửa đề: -103/51*52

\(D=\dfrac{1}{2}+\dfrac{1}{3}-\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{50}+\dfrac{1}{51}-\dfrac{1}{51}-\dfrac{1}{52}\)

=1/2-1/52

=26/52-1/52=25/52

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

`3S =  1.2.3 + 2.3.(4-1) + 3.4.(5-4) + 4.5.(6-3) + ... + 99.100.(101-98)`

`3S =  1.2.3 + 2.3.4-1.2.3 + 3.4.5-4.5.6 + 4.5.6-3.4.5 + ... + 99.100.101-98.99.100`

`3S =  99.100.101`

`S = 33.100.101`

`S = 333300`

3S=1.2(3-0)+2.3(4-1)+.....+99.100(101-98)

=1.2.3-0.1.2+2.3.4-1.2.3+4.5.6-2.3.4+....+99.100.101-98-99-100

=99.100.101

S=33.100.101

=333300

ta có :