a = 1.2 +2.3+3.4+..... +19.20
tính A.3
Tính
a) S= 1.2+2.3+3.4+...+32.33
b) S= 1.2+2.3+3.4+...+49.50
Ta có : S = 1.2 + 2.3 + 3.4 + ..... + 32.33
=> 3S = 1.2.3 - 1.2.3 + 2.3.4 - 2.3.4 + ...... + 32.33.34
=> 3S = 32.33.34
=> S = \(\frac{32.33.34}{3}=11968\)
Tính :
a) ( 12 + 22 + 32 +....+ 492 ) - ( 1.2 + 2.3 + 3.4+....+ 49.50 )
b) Tính A - B =... biết A =1.2 + 2.3 + 3.4 + ...+ 98.99 và B = 1^2 + 2^2 + 3^2 +...+98^2?
Cho A=1/1.2 + 1/2.3 + + 1/ 3.4+...+1/49.50 ; B = 1.2+2.3+3.4+4.5+5.6+...+49.50
Tính 50 mủ 2 A – B/17
1.Tính
A= (1-1/22).(1-1/32)...(1-1/1002)
B= -1/1.2-1/2.3-1/3.4-...-1/100.101
C= 1.2+2.3+3.4+...+100.101
Lời giải :
Đặt S=1.2+2.3+3.4+4.5+…+99.100+100.101
3S=1.2.3+2.3.3+3.4.3+4.5.3+…+99.100.3+100.101.3
=1.2(3−0)+2.3(4−1)+3.4(5−2)+4.5(6−3)+…+99.100(101−98)+100.101(102−99)
=0.1.2-1.2.3+1.2.3-2.3.4+...+99.100.101-100.101.102
=100.101.102
S=100.101.34=343400
1.Tính
a) Ta có:
A=(1-1/22).(1-1/32)...(1-1/1002)
=>A=3/22.8/32.....9999/1002
=>A=(1.3/2.2).(2.4/3.3).....(99.101/100.100)
=>A=(1.2.3.....99/2.3.4.....100).(3.4.5.....101/2.3.4.....100)
=>A=1/100.101/2
=>A=101/200
b) Ta có:
B=-1/1.2-1/2.3-1/3.4-...-1/100.101
=>B=-(1/1.2+1/2.3+1/3.4+...+1/100.101)
=>B=-(1-1/2+1/2-1/3+1/3-1/4+...+1/100-1/101)
=>B=-(1-1/101)
=>B=-100/101
c) Ta có:
C=1.2+2.3+3.4+...+100.101
=>3C=1.2.3+2.3.3+3.4.3+...+100.101.3
=>3C=1.2.3+2.3.(4-1)+3.4.(5-2)+...+100.101.(102-99)
=>3C=1.2.3-1.2.3+2.3.4-2.3.4+3.4.5-3.4.5+...+100.101.102
=>3C=100.101.102
=>3C=1030200
=>C=343400
Chúc bạn hok tốt nhé >:)!!!!!
cho A = 1.2+2.3+3.4+..................+19.20
tính A . 3 = ?
A x 3 = 1.2.3 + 2.3.3 + ...+ 19.20.3
A x 3 = 1.2.( 3 - 1) + 2.3.(4 - 1) + ...+ 19.20.( 21-18)
A x 3 = ( 1.2.3 + 2.3.4 + ....+ 19.20.21) - ( 0.1.2 + 1.2.3 + ....+ 18.19.20)
=> A x 3 = 19 x 20 x 21 = 7890
\(3A=1.2.3+2.3.3+....+19.20.3\)
\(3A=1.2.\left(3-0\right)+2.3.\left(4-1\right)+....+19.20\left(21-18\right)\)
\(3A=1.2.3-1.2.0+2.3.4-2.3.1+....+19.20.21-19.20.18\)
ta có thể thấy 1.2.3 = 2.3.1 và những con số khác cũng vậy
\(\Rightarrow3A=19.20.21\)
mink nghĩ vậy bạn ạ, sai đừng trách mink nha
1. a) Tính tổng :
D = 1.2 + 2.3+ 3.4 +...+ 99.100
b) Chứng minh:
Dn = 1.2 + 2.3 + 3.4 +...+ n (n +1)
= n (n + 1) . (n + 2) : 3 ( với n thuộc N*)
D = 1.2 + 2.3+ 3.4 +...+ 99.100
=>3D=1.2.3+2.3.3+3.4.3+...+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
=99.100.101-0.1.2
=99.100.101
=999900
=>D=999900:3=333300
Dn = 1.2 + 2.3 + 3.4 +...+ n (n +1)
=>3Dn=1.2.3+2.3.3+3.4.3+...+n(n+1).3
=1.2.(3-0)+2.3.(4-1)+3.4.(5-2)+...+n.(n+1).[(n+2)-(n-1)]
=1.2.3-0.1.2+2.3.4-1.2.3+2.3.4-2.3.4+....+n(n+1)(n+2)-(n-1)n(n+1)
=n.(n+1).(n+2)-0.1.2
=n.(n+1)(n+2)
=>Dn=n.(n+1)(n+2):3
=>điều cần chứng minh
giúp mình bài này với: A=3/1.2+3/2.3+3/3.4+3/4.5+...+3/2021.2022
A=3/1.2+3/2.3+3/3.4+3/4.5+...+3/2021.2022
A=3(1/1.2+1/2.3+1/3.4+1/4.5+...+1/2021.2022)
A=3(1/1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+...+1/2021-1/2022)
A=3[1/1+(1/2-1/2)+(1/3-1/3)+(1/4-1/4)+...+(1/2021-1/2021)-1/2022]
A=3[1/1+0+0+0+...+0-1/2022
A=3(1/1-1/2022)
A=3(2022/2022-1/2022)
A=3.2021/2022
A=2021/674
Bn Tham Khảo:
https://hoc247.net/hoi-dap/toan-6/tinh-tong-s-3-1-2-3-2-3-3-3-4-3-4-5-3-2015-2016-faq188428.html
A= 1.2+2.3+3.4+...........+ 2020.2021
A=1.2+2.3+3.4+...+99.100
3S=1*2*3+2*3*(4-1)+...+99*100*(101-98)
=1*2*3+2*3*4-1*2*3+...+99*100*101-99*100*98
=99*100*101
=>S=33*100*101=333300