Question

A=1x2+2x3+3x4+...+49x50

B=1x3+3x5+5x7+...+99x101

C=1x2x3+2x3x4+3x4x5+...+50x51x52

D=1x4+2x5+3x6+...+60x63

E=1x1+2x2+3x3+...+50x50

F=1x1+3x3+5x5+...+71x71

G=1x1+4x4+7x7+...+100x100

I=1x2x3+3x4x5+5x6x7+...+69x70x71

Answer 1

A=1x2+2x3+3x4+...+49x50

3A= 3(1.2+2.3+3.4+...+49.50)

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

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

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

A= 49.50.51/3=41650

Answer 2

B=1x3+3x5+5x7+...+99x101

B=1/1.3 +1/3.5 +...+1/99.101

2B=2/1.3 + 2/3.5 +...+2/99.101

2B=1-1/3+1/3-1/5+...+1/99-1/101

2B=1-1/101

2B=100/101

B=100/101:2=100/202

Answer 3

C=1x2x3+2x3x4+3x4x5+...+50x51x52
Nhân C với 4 ta được:
C x 4 = 1x2x3x4 + 2x3x4x 4 + 3x4x5x4 +…+50x51x52x4
C x 4 = 1x2x3x4 + 2x3x4x(5-1) + 3x4x5x(6-2) + ... + 50x51x52x(53-49)
C x 4 = 1x2x3x4 + 2x3x4x5 - 1x2x3x4 + 3x4x5x6 - 2x3x4x5 + ... +49x 50x51x52 - 50x51x52x53
Sau khi cộng - trừ giản ước ta có : C x 4 = 50x51x52x53
C = 50x51x52x53 : 4 = 1756950

Answer 4

E=1x1+2x2+3x3+...+50x50

E = 1 x (2-1) + 2x (3-1) +.....+ 50x(51-1)

E = (1 x 2 +2 x 3 + .... + 50x51 ) - ( 1 + 2 + .... +50 )

E=                        P                                  -             Q

P x 3 = 1x2x3 + 2x3x3 + ..... + 50x51 x3

P x 3 =1x2x(3-0) + 2x3x(4-1) +....+ 50x51 x ( 52-49)

P x 3 = 1x2x3 + 2x3x4 - 1x2x3 +......+ 49x50x51-50x51x52

P x 3 = 50x51x52 

P = 50x17x52 = 44200

Q = 1 + 2 + 3 + ..... + 50 ( Có 50 số )

Q = ( 50 + 1 ) x 50 : 2 = 1275 

P - Q = E = 44200 - 1275 =42475 

Answer 5

1x4+2x5+3x6+4x7+...47x50