A=1.2.3+2.3(4-1)+3.4(5-2)+4.5(6-3)+....+98.99(100-97)   "." la dau nhan

A=1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+4.5.6-3.4.5+....+98.99.100-97.98.99

A=1.2.3+98.99.100

A= 970206

Ta có : B = 1.2 + 2.3 + 3.4 + ..... + 98.99

=> 3B = 0.1.2 + 1.2.3 - 1.2.3 + ...... + 98.99.100

=> 3B = 98.99.100

=> B = \(\frac{98.99.100}{3}\)  = 323400

C = 1.1 + 2.2 + 3.3 + ..... + 98.98

=> C = 1.(2 - 1) + 2(3 - 1) + 3(4 - 1) + ...... + 98(99 - 1)

=> C = 1.2 - 1 + 2.3 - 2 + 3.4 - 3 + ..... + 98.99 - 98

=> C = (1.2 + 2.3 + 3.4 + ..... + 98.99) - (1 + 2 + 3 + ..... + 98) 

=> C = 323400 - 4851

=> C = 318549. 

 nào lm đúng nhanh nhất mk cho  2 k lun

b1. 456 = 10.(40+5)+6

A = 10( 44.....440 + 55....55) + 66..66    (... 111 số)

=499.....9950 + 66...66     (... 111 số 9 và 111 số 6)

= 55....5516 (....111 số 5)

b2. A - B = 1+2 + 3 + 4 +....+98 = 49 x100 + 51 = 4951 

Câu a vô lí quá , phần tử khong cho là bao nhiêu số làm sao tính được

\(b=1.1+2.2+...+98.98=1\left(2-1\right)+2\left(3-1\right)+..+98.\left(99-1\right)=\left(1.2+2.3+...+98.99\right)-\left(1+2+...+98\right)\)=> \(a-b=\left(1.2+2.3+..+98.99\right)-\left[\left(1.2+2.3+...+98.99\right)-\left(1+2+...+98\right)\right]=1+2+3+...+98\)ta tính tổng của dãy số: a-b= (98+1).98:2=4851

A = 1x2 + 2x3 + 3x4 + 4x5 + ...+ 99x100

A x 3 = 1x2x3 + 2x3x3 + 3x4x3 + 4x5x3 + ... + 99x100x3

A x 3 = 1x2x3 + 2x3x(4-1) + 3x4x(5-2) + 4x5x(6-3) + ... + 99x100x(101-98)

A x 3 = 1x2x3 + 2x3x4 - 1x2x3 + 3x4x5 - 2x3x4 + 4x5x6 - 3x4x5 + ... + 99x100x101 - 98x99x100.

A x 3 = 99x100x101

A = 99x100x101 : 3

A = 333300

B = ... (bạn tự tính)

=> A - B = ...

...

ta co 1^2+

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

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

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

\(\frac{2}{1.2}+\frac{2}{2.3}+\frac{2}{3.4}+....+\frac{2}{99.100}\)

= \(2\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+....+\frac{1}{99.100}\right)\)

= \(2.\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+....+\frac{1}{99}-\frac{1}{100}\right)\)

= \(2.\left(1-\frac{1}{100}\right)\)

= \(2.\frac{99}{100}\)

= \(\frac{99}{50}\)

chịu thua