1.2.3+2.3.4+......+98.99.100
TÍNH TỔNG NHA KO GIẢI PHƯƠNG TRÌNH NHÉ
K
Khách
Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
Những câu hỏi liên quan
12 tháng 8 2017
Đặt \(A=\frac{1}{1.2.3}+\frac{1}{2.3.4}+....+\frac{1}{2005.2006.2007}\)
\(B=1.2+2.3+3.4+....+2006.2007\)
Ta có : \(A=\frac{1}{2}\left(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+....+\frac{1}{2005.2006}-\frac{1}{2006.2007}\right)\)
\(=\frac{1}{2}\left(\frac{1}{1.2}-\frac{1}{2006.2007}\right)\)
\(B=1.2+2.3+3.4+....+2006.2007\)
\(=\frac{1.2.3+2.3.\left(4-1\right)+3.5.\left(5-2\right)+...+2006.2007.\left(2008-2005\right)}{3}\)
\(=\frac{1.2.3+2.3.4-1.2.3+3.4.5-...+2006.2007.2008-2005.2006.2007}{3}\)
\(=\frac{2006.2007.2008}{3}\)
\(\Rightarrow\frac{1}{2}\left(\frac{1}{2}-\frac{1}{2006.2007}\right)x=\frac{2006.2007.2008}{3}\)
\(\Rightarrow x=\frac{2006.2007.2008}{3}:\left[\frac{1}{2}\left(\frac{1}{2}-\frac{1}{2006.2007}\right)\right]\)(tự tính)
24 tháng 3 2016
= 1/2*(1/1*2 - 1/2*3 + 1/2*3 - 1/3*4 + ... + 1/8*9 - 1/9*10) = 1/2*(1/1*2 - 1/9*10)=1/2 * 22/45 = 11/45
24 tháng 3 2016
2A = \(\frac{1}{1\cdot2}-\frac{1}{2\cdot3}+\frac{1}{2\cdot3}-\frac{1}{3\cdot4}+...+\frac{1}{8\cdot9}-\frac{1}{9\cdot10}\)
2A = \(\frac{1}{2}-\frac{1}{90}\)
2A = \(\frac{44}{90}\)
A = \(\frac{22}{90}\)
6 tháng 3 2019
\(D=\frac{1}{1\cdot2\cdot3}+\frac{1}{2\cdot3\cdot4}+\frac{1}{3\cdot4\cdot5}+...+\frac{1}{10\cdot11\cdot12}\)
\(D=\frac{1}{2}\left(\frac{2}{1\cdot2\cdot3}+\frac{2}{2\cdot3\cdot4}+\frac{2}{3\cdot4\cdot5}+...+\frac{2}{10\cdot11\cdot12}\right)\)
\(D=\frac{1}{2}\left(\frac{1}{1\cdot2}-\frac{1}{2\cdot3}+\frac{1}{2\cdot3}-\frac{1}{3\cdot4}+\frac{1}{3\cdot4}-\frac{1}{4\cdot5}+...+\frac{1}{10\cdot11}-\frac{1}{11\cdot12}\right)\)
\(D=\frac{1}{2}\left(\frac{1}{2}-\frac{1}{132}\right)=...\)
IA
6 tháng 3 2019
\(D=\frac{1}{1.2.3}+\frac{1}{2.3.4}+\frac{1}{3.4.5}+...+\frac{1}{10.11.12}\)
\(D=\left(\frac{2}{1.2.3}+\frac{2}{2.3.4}+\frac{2}{3.4.5}+...+\frac{2}{10.11.12}\right).\frac{1}{2}\)
\(D=\left(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+\frac{1}{3.4}-\frac{1}{4.5}+...+\frac{1}{10.11}-\frac{1}{11.12}\right).\frac{1}{2}\)
\(D=\left(\frac{1}{1.2}-\frac{1}{11.12}\right).\frac{1}{2}\)
\(D=\frac{65}{132}.\frac{1}{2}\)
\(D=\frac{65}{264}\)
TZ
1
8 tháng 11 2015
Đặt A= 1.2+2.3+...+99.100
=>3A=1.2.3+2.3.3+...+99.100.3
=>3A=1.2.3+2.3.(4-1)+...+99.100.(101-98)
=>3A=1.2.3+2.3.4-1.2.3+...+99.100.101-98.99.100
=>3A=99.100.101
=>3A=999900
=>A=999900:3
=>A=333300
TZ
0
ND
2
H
9 tháng 9 2023
https://hoc247.net/hoi-dap/toan-6/tinh-tong-s-1-1-2-3-1-2-3-4-1-n-n-1-n-2--faq240420.html
`->` Mình tham khảo ở đây để làm nếu sai thì cho mik xl ạ.
Đặt \(A=\dfrac{1}{1\cdot2\cdot3}+\dfrac{1}{2\cdot3\cdot4}+....+\dfrac{1}{\left(n-2\right)\cdot\left(n-1\right)\cdot n}\)
\(2A=\dfrac{2}{1\cdot2\cdot3}+\dfrac{2}{2\cdot3\cdot4}+...+\dfrac{2}{\left(n-2\right)\cdot\left(n-1\right)\cdot n}\\ 2A=\dfrac{1}{1\cdot2}-\dfrac{1}{2\cdot3}+\dfrac{1}{2\cdot3}-\dfrac{1}{3\cdot4}+....+\dfrac{1}{\left(n-2\right)\cdot\left(n-1\right)}-\dfrac{1}{\left(n-1\right)\cdot n}\)
\(2A=\dfrac{1}{1\cdot2}-\dfrac{1}{\left(n-1\right)\cdot\left(n-2\right)}\)
\(A=\dfrac{1}{4}-\dfrac{1}{\left(n-1\right)\cdot\left(n-2\right)\cdot2}\)
T
9 tháng 9 2023
\(\dfrac{1}{1\cdot2\cdot3}+\dfrac{1}{2\cdot3\cdot4}+\cdot\cdot\cdot+\dfrac{1}{\left(n-2\right)\cdot\left(n-1\right)\cdot n}\)
\(=\dfrac{1}{2}\left(\dfrac{2}{1\cdot2\cdot3}+\dfrac{2}{2\cdot3\cdot4}+\cdot\cdot\cdot+\dfrac{2}{\left(n-2\right)\cdot\left(n-1\right)\cdot n}\right)\)
\(=\dfrac{1}{2}\left[\dfrac{1}{1\cdot2}-\dfrac{1}{2\cdot3}+\dfrac{1}{2\cdot3}-\dfrac{1}{3\cdot4}+\cdot\cdot\cdot+\dfrac{1}{\left(n-2\right)\left(n-1\right)}-\dfrac{1}{\left(n-1\right)n}\right]\)
\(=\dfrac{1}{2}\left[\dfrac{1}{1\cdot2}-\dfrac{1}{\left(n-1\right)n}\right]\)
\(=\dfrac{1}{2}\cdot\left[\dfrac{n\left(n-1\right)}{2n\left(n-1\right)}-\dfrac{2}{2n\left(n-1\right)}\right]\)
\(=\dfrac{1}{2}\cdot\dfrac{n\left(n-1\right)-2}{2n\left(n-1\right)}\)
\(=\dfrac{n^2-n-2}{4n\left(n-1\right)}\)
#\(Toru\)
9 tháng 10 2015
ta đặt: A = 1/1.2.3 + 1/2.3.4 + 1/3.4.5 +...+ 1/2005.2006.2007
2.A = 2(1/1.2.3 + 1/2.3.4 + 1/3.4.5 +...+ 1/2005.2006.2007)
2.A = 2/1.2.3 + 2/2.3.4 + 2/3.4.5 +...+ 2/2005.2006.2007
= (1/1.2 - 1/2.3) + (1/2.3 - 1/3.4) +...+ (1/2005.2006- 1/2006.2007)
= 1/1.2 - 1/2.3 + 1/2.3 - 1/3.4 + ... +1/2005.2006 - 1/2006.2007
= 1/1.2 - 1/2006.2007
=> A = (1/1.2 - 1/2006.2007):2
A = 1/4 - 1/1003.2007
Đặt B = 1/1.2 + 1/2.3+ 1/ 3.4 ..... + 1/2006.2007
=(1/1-1/2)+(1/2-1/3)+(1/3-1/4)+....+(1/2006-1/2007)
=1/1-1/2+1/2-1/3+1/3-1/4+....+1/2006-1/2007
=1/1-1/2007
= 2006/2007
thay vào phương trình ta có phương trình trở thành:
(1/4 - 1/1003.2007).x = 2006/2007
..........
còn lại bạn tính nhé
BT
7 tháng 8 2017
Ta có:
\(\frac{2}{1.2.3}=\frac{1}{1.2}-\frac{1}{2.3}\); \(\frac{2}{2.3.4}=\frac{1}{2.3}-\frac{1}{3.4}\); ...; \(\frac{2}{2005.2006.2007}=\frac{1}{2005.2006}-\frac{1}{2006.2007}\)
\(A=\frac{1}{2}\left(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+...+\frac{1}{2005.2006}-\frac{1}{2006.2007}\right)=\frac{1}{2}\left(\frac{1}{2}-\frac{1}{2006.2007}\right)\)
\(A=\frac{1}{2}\left(\frac{1003.2007-1}{2006.2007}\right)\)
B=1.2+2.3+3.4+...+2006.2007=\(\frac{2006.2007.2008}{3}\)
Ta có: A.x=B => x=B:A = \(\frac{2006.2007.2008}{3}:\left\{\frac{1}{2}.\frac{1003.2007-1}{2006.2007}\right\}=\frac{2006.2007.2008}{3}.\frac{2.2006.2007}{1003.2007-1}\)
=> \(x=\frac{2.2006^2.2007^2.2008}{6039060}=2676.2007^2\)