Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
ta có
1=1
1/1.2 =1-1/2
1/2.3 1/2-1/3
1/3.4 =1/3-1/4
.......
1/(99.100) =1/99 -1/100
cộng theo vế các đẳng thức trên được
S =1+1-1/2+1/2-1/3+1/3-1/4+...+1/99-1/100
S =2-1/100
Bài giải:
Đặt A = 1.2 + 2.3 + 3.4 + ....+ 99.100
3A = 1.2.3 + 2.3.4 + 3.4.5 + ....+ 99.100.3
3A = 1.2.(3 - 0) + 2.3.(4 - 1) + 3.4.(5 - 2)...... . 99.100. (101 - 98)
3A = (1.2.3 + 2.3.4 + 3.4.5 + ... + 99.100.101) - (0.1.2 + 1.2.3 + 2.3.4 + ... + 98.99.100)
3A = 99.100.101 - 0.1.2
3A = 999900 - 0
3A = 999900
A = 999900 : 3
A = 333300
A=1.2+2.3+...+99.100
3A=1.2.3+2.3.4+3.4.3+...+99.100.3
3A=1.2.(3-0)+2.3.(4-1)+3.4.(5-2)+...+99.100.(101-98)
3A=(1.2.3+2.3.4+3.4.5+...+99.100.101)-(0.1.2+1.2.3+2.3.4+...+98.99.100
3A=99.100.101-0.1.2
3A=999900-0
3A=999900
A=999900:3
A=333300
A = 1.2+2.3+3.4+......+99.100
Gấp A lên 3 lần ta có:
A . 3 = 1.2.3 + 2.3.3 + 3.4.3 + … + 99.100.3
A . 3 = 1.2.3 + 2.3.(4 - 1) + 3.4.( 5 - 2) + … + 99.100. (101 - 98)
A . 3 = 1.2.3 + 2.3.4 - 1.2.3 + 3.4.5 - 2.3.4 + … + 99.100.101 - 98.99.100
A . 3 = 99.100.101
A = 99.100.101 : 3
A = 33.100.101
A = 333 300
Đặt A = 1.2 + 2.3 + 3.4 + ...+99.100
=> 3A = 1.2.3 + 2.3.3 + 3.4.3 + ... + 99.100.3
=> 3A = 1.2.3 + 2.3.(4-1) + 3.4.(5-2) + ... + 99.100.(101-98)
=> 3A = 1.2.3 + 2.3.4 - 1.2.3 + 3.4.5 - 2.3.4 + 4.5.6 - 3.4.5 + ... + 99.100.101-98.99.100
=> 3A = 1.2.3 - 1.2.3 + 2.3.4 - 2.3.4 + 3.4.5 - 3.4.5 + ... + 99.100.101
=> 3A = 99.100.101
=> 3A = 999900
=> A = 999900 : 3
=> A = 333300
Vậy A = 333300
A = 1.2 + 2.3 + 3.4 + .. + 99.100
<=> 3A = 1.2.3 + 2.3.3 + 3.4.3 +...+ 99.100.3
= 1.2.3 + 2.3.(4-1) + 3.4.( 5 -2) +...+ 99.100.(101-98)
= 1.2.3 - 1.2.3 + 2.3.4 - 2.3.4 + 3.4.5 + ..- 98.99.100 + 99.100.101
= 999900
<=> A = 999900 : 3 = 333300
A=1.2+2.3+3.4+...+99.100
3A=1.2.(3-0)+2.3.(4-1)+3.4.(5-2)+...+99.100.(101-98)
3A=1.2.3+2.3.4+3.4.5+...+98.99.100+99.100.101 - 0.1.2-1.2.3-2.3.4-3.4.5-...-98.99.100
3A=99.100.101-0.1.2
3A=999900-0
3A=999900
A=999900:3
A=333300
= 2/1 - 2/2 + 2/2 - 2/3 + 2/3 - 2/4 + ..... + 2/99 - 2/100
= 2/1 + 2/100
= 101/50
Đặt A = 1.2 + 2.3 + 3.4 + .... + 99.100
3A = 1.2.3 + 2.3.3 + 3.4.3 + .... + 99.100.3
= 1.2.3 + 2.3.(4 - 1) + 3.4.(5 - 2) + .... + 99.100(101 - 98)
= 1.2.3 + 2.3.4 - 1.2.3 + 3.4.5 - 2.3.4 + ..... + 99.100.101 - 98.99.100
= 99.100.101
\(\Rightarrow A=\frac{99.100.101}{3}=333300\)
Đặt A = 1.2 + 2.3 + 3.4 + ... + 99.100
3A = 1.2.3 + 2.3.3 + 3.4.3 + .... + 99.100.3
3A = 1.2.3 + 2.3.( 4 - 1 ) + 3.4.( 5 - 2 ) + .... + 99.100.( 101 - 98 )
3A = ( 1.2.3 + 2.3.4 + 3.4.5 + .... + 99.100.101 ) - ( 0.1.2 + 1.2.3 + 2.3.4 + ....+ 98.99.100 )
3A = 99.100.101 - 0.1.2
3A = 999900 - 0
3A = 999900
A = 999900 : 3
A = 333300
A= 1.2+2.3+3.4.....+99.100
=>3A=1.2.3+2.3.3+3.3.4+....+99.100.3
=1.2(3-0)+2.3.(4-1)+3.4.(5-2)+...+99.100.(101-98)
=1.2.3-0.1.2+2.3.4-1.2.3+3.4.5-2.3.4+...+99.100.101-98.99.100
=99.100.101-0
=999900
=>A=999900:3=333300
Ta có:1/1.2+1/2.3+...+1/99.100
=1-1/2+1/2-1/3+...+1/99-1/100
=1-1/100
=100-1/100
=99/100
A . 3 = 1.2.3 + 2.3.3 + 3.4.3 + … + 99.100.3
A . 3 = 1.2.3 + 2.3.(4 - 1) + 3.4.( 5 - 2) + … + 99.100. (101 - 98)
A . 3 = 1.2.3 + 2.3.4 - 1.2.3 + 3.4.5 - 2.3.4 + … + 99.100.101 - 98.99.100
A . 3 = 99.100.101
A = 99.100.101 : 3
A = 33.100.101
A = 333 300
A3=1.2.3+2.3.3+3.4.3+.....+99.100.3
A3=1.2.3+2.3.(4-1)+ 3.4.(5-2)+......+99.100(101-98)
A3=1.2.3+2.3.4-1.2.3+2.3.4+3.4.5+......+99.100.101-98.99.100
A3=99.100.101
A=99.100.101:3
A=333300