vậy mà cũng hỏi

mắc j k... bn biết mà mik k biết thì mik hỏi chứ... VÔ DUYÊN

mình không biết vì...

\(M=\frac{2}{1.2.3}+\frac{2}{2.3.4}+...+\frac{2}{48.49.50}\)

\(M=\frac{1}{1.2}-\frac{1}{2.3}+\frac{2}{2.3}-\frac{1}{3.4}+...+\frac{1}{48.49}-\frac{1}{49.50}\)

\(M=\frac{1}{1.2}-\frac{1}{49.50}\)

\(M=\frac{1}{2}-\frac{1}{2450}=\frac{612}{1225}\)

A  = 1.2.3 + 2.3.4 + ....+ 48.49.50

=> 4A = 1.2.3.4 + 2.3.4.(5-1) + ...+ 48.49.50.(51-17)

= 1.2.3.4 + 2.3.4.5 - 1.2.3.4 + .....+ 48.49.50.51 - 47.48.49.50

= 48.49.50.51

=> A =  48.49.50.51:4 = 12.49.50.51

bài b) làm tương tự nha

\(C=1.2.3+2.3.4+...+48.49.50\)

\(\Rightarrow4C=1.2.3.4+2.3.4.4+...+48.49.50.4\)

\(=1.2.3.4+2.3.4.\left(5-1\right)+...+48.49.50.\left(51-47\right)\)

\(=1.2.3.4+2.3.4.5-1.2.3.4+...+48.49.50.51-47.48.49.50\)

\(=48.49.50.51\)

\(\Rightarrow C=\frac{48.49.50.51}{4}=1499400\)

tao có:

2p=2/1.2.3+2/2.3.4+...+2/n.n(+1)n(n+2)

2p=3-1/1.2.3+4-2/1.2.3+...+(n+2)-n/n.(n+1).(n+2)

2p=3/1.2.3-1/1.2.3+4/2.3.4-2/2.3.4+...+(n+2)/n.(n+1).(n+2)-n/n.(n+1).(n+2)

2p=1/1.2-1/2.3+1/2.3-1/3.4+...+1/n.(n+1)-1/(n+1).(n+2)

2p=1/1.2-1/(n+1).(n+2)

2p=(n+!).(n+2)-2/(2n+2).(n+2)

suy ra p=(n+1).(n+2)-2/(2n+2).(2n+4)

2s=3-1/1.2.3+4-2/1.2.3+...+50-48/48.49.50

2s=3/1.2.3-1/1.2.3+4/2.3.4-2/2.3.4+...+50/49.50.48-48/48.50.49

2s=1/1.2-1/2.3+1/2.3-1/3.4+...+1/48.49-1/49.50

2s=1/1.2-1/49.50

'2s=1/2-1/2450

2s=1225/2450-1/2450

2s=1224/2450

s=612/1225

\(P=\frac{1}{1\cdot2\cdot3}+\frac{1}{2\cdot3\cdot4}+\frac{1}{3\cdot4\cdot5}+...+\frac{1}{n\left(n+1\right)\left(n+2\right)}\)1

\(P=\frac{1}{2}\left(\frac{2}{1\cdot2\cdot3}+\frac{2}{2\cdot3\cdot4}+\frac{2}{3\cdot4\cdot5}+...+\frac{2}{n\left(n+1\right)\left(n+2\right)}\right)\)

\(P=\frac{1}{2}\left(\frac{1}{1\cdot2}-\frac{1}{2\cdot3}+\frac{1}{2\cdot3}-\frac{1}{3\cdot4}+\frac{1}{3\cdot4}-\frac{1}{4\cdot5}+...+\frac{1}{n\left(n+1\right)}-\frac{1}{\left(n+1\right)\left(n+2\right)}\right)\)

\(P=\frac{1}{2}\left(\frac{1}{2}-\frac{1}{\left(n+1\right)\left(n+2\right)}\right)\)

\(P=\frac{\left(\frac{1}{2}-\frac{1}{\left(n+1\right)\left(n+2\right)}\right)}{2}\)

S cx tinh giong v

I don't now

mik ko biết 

sorry 

......................

b,\(B=2^2+4^2+...+20^2\)

\(\Rightarrow B=2^2\left(1^2+2^2+...+10^2\right)\)

\(\Rightarrow B=4.\left[1.\left(2-1\right)+2.\left(3-1\right)+...+10.\left(11-1\right)\right]\)

\(\Rightarrow B=4\left(1.2-1+2.3-2+...+10.11-10\right)\)

\(\Rightarrow B=4\left[\left(1.2+2.3+...+10.11\right)-\left(1+2+...+10\right)\right]\)

\(\Rightarrow B=4\left(\frac{10.11.12}{3}-\frac{11.10}{2}\right)\)

c)C=(1.2+2.3+3.4+...+20.21)-(1²+2²+3²+...+20²)

=>C=1.2+2.3+3.4+...+20.21-1.1-2.2-3.3-...-20.20

=>C=1.(2-1)+2.(3-2)+3.(4-3)+...+20.(21-20)

=>C=1+2+3+...+20

=>C=(1+20)+(2+19)+...+(15+16)

=>C=21+21+...+21

=>C=21.10

=>C=210

a) A = 1.3 +2.4 + 3.5 +...+ 97.99 + 98.100

A = 1(2 + 1) + 2(3+1) + 3(4 + 1) +...+ 98(99+1)

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

= [ 1.2.3 + 2.3.(4-1) +...+ 98.99.(100-97)] + [ 1.2 + 2.(3-1) + 3.(4-2) +... 98.(99-97)]

= [ 1.2.3 + 2.3.(4-1) - 1.2.3 + 3.4.(5-2) - 2.3.(4-1) +...+ 98.99.(100-97) - 97.98(99-96)] + [ 1.2 + 2.(3-1) - 1.2 + 3.(4-2) - 2.(3-1) +...+ 98.(99-97) - 97(98-96)]

= 98.99.100:3 + 98.99:2 = 323 400 + 4581 = 328251

b) B = 1.2.3 + 2.3.4 + 3.4.5 +...+ 48.49.50

4B = 1.2.3.4 + 2.3.4.(5-1) + 3.4.5.(6-2) +...+ 48.49.50.(51-47)

4B-B = 1.2.3.4 + 2.3.4.(5-1) - 1.2.3.4 + 3.4.5.(6-2) - 2.3.4.(5-1) +...+ 48.49.50.(51-47) - 47.48.49.(50-46)

= 48.49.50.51:4 = 1499400

c) C = 1/2 + 1/2^2 + 1/2^3 +...+ 1/2^10

=> 2C = 1 + 1/2 + 1/2^2 +...+ 1/2^9 (1)

= 1/2 + 1/2^2 +...+ 1/2^10

Lấy (1)-(2) ta được:

A = 1-1/2^10 = 1024/1024 - 1/1024 = 1023/1024

Chúc bạn học tốt

a) A = 1.( 2 + 1 ) + 2.( 3 + 1 ) + 3.( 4 + 1 ) + ...+ 98.( 99 + 1 )

A = 1.2 + 1 + 2.3 + 2 + 3.4 + 3 + ... + 98.99 + 98

A = ( 1.2 + 2.3 + 3.4 + ... + 98.99 ) + ( 1 + 2 + 3 + 4 + ... + 98 )

Dat B = 1.2 + 2.3 + 3.4 + ...+ 98.99

      C = 1 + 2 + 3 + 4 + ... + 98

=> 3B = 1.2.3 + 2.3.3 + 3.4.3 + ...+ 98.99.3

          = 1.2.3 + 2.3.( 4 - 1 ) + 3.4.( 5 - 2 ) + ....+ 98.99.( 100 - 97 )

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

=> B = ( 98.99.100 ) : 3 = 323400

=> C = 1 + 2 + 3 + ... 98

     C = 98 + 97 + ...+ 3 + 2 + 1

Tu lam tiep nha

a)

A= 1.2 +1.2.3+2+3.4+3+......98.99+98

A=(1.2+2.3+3.4+........98.99)+(1+2+3+4+...98)

\(A=1.2.3+2.3.4+3.4.5+...+48.49.50\)

\(4A=1.2.3.4+2.3.4.4+3.4.5.4+...+48.49.50.4\)

\(4A=1.2.3.\left(4-0\right)+2.3.4.\left(5-1\right)+...+48.49.50.\left(51-47\right)\)

\(4A=1.2.3.4-0.1.2.3+2.3.4.5-1.2.3.4+...+48.49.50.51-48.48.49.50\)

\(4A=48.49.50.51\)

\(A=\dfrac{48.49.50.51}{4}=1499400\)

A=1499400 nhe ban !

4A=4.[1.2.3 + 2.3.4 + 3.4.5 + 4.5.6 + . . . . . . + 48.49.50]
4A=1.2.3.4 +2.3.4.4 +3.4.5.4 +4.5.6.4 +.........+48.49.50.4
4A=1.2.3.4 +2.3.4.(5-1) + 3.4.5.(6-2) +4.5.6(7-3)+....+ 48.49.50(51-47)
4A=1.2.3.4 +2.3.4.5 --1.2.3.4 + 3.4.5.6--2.3.4.5 + 4.5.6.7-3.4.5.6+....+ 48.49.50.51--47.48.49.50
4A =48.49.50.51
A=(48.49.50.51)/4