Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
\(\frac{315}{316}\cdot\frac{316}{314}\cdot\frac{316}{315}\cdot\frac{317}{313}=\frac{315.316.316.317}{316.314.315.313}=\frac{1.1.316.317}{1.314.1.313}=\frac{100172}{98282}\)
Ta có : \(\frac{3}{2}\times\frac{4}{5}\times\frac{2}{3}\)
\(=\frac{3}{2}\times\frac{2}{3}\times\frac{4}{5}=1\times\frac{4}{5}\)
\(=\frac{4}{5}\)
6 2/7 + 7 3/5 + 8 6/9 + 9 1/4 + 2/5 + 5/7 + 1/3 x 3/4 + 1967
= 44/7 + 38/5 + 78/9 + 37/4 + 2/5 + 5/7 + 1/3 + 1967
= ( 44/7 + 5/7 ) + ( 38/5 + 2/5 ) + ( 26/3 + 1/3 ) + ( 37/4 + 3/4 ) +1967
= 7 + 8 + 9 + 10 + 1967
= 15 + 9 + 10 + 1967
= 24 + 10 + 1967
= 34 + 1967
= 2001
đầu bài là ê các bạn mình thấy lạ thật đấy chưa từng thấy đầu bài nào kì cục như vậy
a = 1/2 nhân 2 + 1/3 nhân 3 + 1/4 nhân 4 + .....+ 1/2009 nhân 2009 + 1/2010 nhân 2010
so sánh a với 1
a=1/2.2+1/3.3+1/4.4+...+1/2009.2009+1/2010.2010(có 2009 số hạng)
a=1+1+1+...+1+1(2009 số 1)
a=1.2009=2009
Vậy a>1
= ( 1 + 3 + 5 + ... + 2011 ) - ( 2 + 6 + 8 + ... + 2010 )
= [ 1006 x ( 2011 + 1 ) : 2 ] - [ 1005 x ( 2010 + 2 ) : 2 ]
= ( 1006 x 2012 : 2 ) - ( 1005 x 2012 : 2 )
= ( 2024072 : 2 ) - ( 2022060 : 2 )
= 1012036 - 1011030
= 1006
a) \(\frac{1}{3}+\frac{5}{6}:\left(x-2\frac{1}{5}\right)=\frac{3}{4}\)
=> \(\frac{1}{3}+\frac{5}{6}:\left(x-\frac{11}{5}\right)=\frac{3}{4}\)
=> \(\frac{5}{6}:\left(x-\frac{11}{5}\right)=\frac{3}{4}-\frac{1}{3}\)
=> \(\frac{5}{6}:\left(x-\frac{11}{5}\right)=\frac{5}{12}\)
=> \(x-\frac{11}{5}=\frac{5}{6}:\frac{5}{12}\)
=> \(x-\frac{11}{5}=2\)
=> \(x=2+\frac{11}{5}\)
=> \(x=\frac{21}{5}\)
\(\frac{3}{5}.\frac{4}{7}.1.\frac{1}{2}\)
\(=\frac{3.4.1.1}{5.7.1.2}\)
\(=\frac{12}{70}\)
\(=\frac{12:2}{70:2}=\frac{6}{35}\)
1/1x2 + 1/2x3+ 1/3x4+....+1/2009x2010
= 1/1-1/2 + 1/2-1/3+ 1/3-1/4+...+1/2009-1/2010
= 1/1-1/2010
= 2009/2010
\(\frac{1}{1\cdot2}+\cdot\cdot\cdot+\frac{1}{2009\cdot2010}\)
\(=1-\frac{1}{2}+\cdot\cdot\cdot+\frac{1}{2009}-\frac{1}{2010}\)
\(=1-\frac{1}{2010}\)
\(=\frac{2009}{2010}\)
2/ 3x5+ 2/5x7+ 2/7x9+...+2/2007x2011+ 2/2011x2013
= 1/3-1/5+ 1/5-1/7+ 1/7-1/9+...+1/2007-1/2011+ 1/2011- 1/2013
= 1/3-1/2013
= 670/2013
Ta có:
\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+....+\frac{1}{2009.2010}\)
= \(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{2009}-\frac{1}{2010}\)
= \(1-\frac{1}{2010}=\frac{2009}{2010}\)
\(\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+....+\frac{2}{2009.2011}+\frac{2}{2011.2013}\)(xem lại đề)
= \(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{2009}-\frac{1}{2011}+\frac{1}{2011}-\frac{1}{2013}\)
= \(\frac{1}{3}-\frac{1}{2013}=\frac{670}{2013}\)
\(\frac{1}{1.2}+....+\frac{1}{2009.2010}\)
\(=1-\frac{1}{2}+...+\frac{1}{2009}-\frac{1}{1010}\)
\(=1-\frac{1}{1010}\)
\(=\frac{2009}{2010}\)
mấy câu kia tương tự
\(\frac{2}{3\times5}+\cdot\cdot\cdot+\frac{2}{2011\times2013}\)
\(=\frac{1}{3}-\frac{1}{5}+\cdot\cdot\cdot+\frac{1}{2011}-\frac{1}{2013}\)
\(=\frac{1}{3}-\frac{1}{2013}\)
\(=\frac{670}{2013}\)
Phần cuối hình như sai sai
\(\frac{1}{1\times4}+\cdot\cdot\cdot+\frac{1}{316\times319}\)
\(=\left(\frac{3}{1\times4}+\cdot\cdot\cdot+\frac{3}{316\times319}\right):3\)
\(=\left(1-\frac{1}{4}+\cdot\cdot\cdot+\frac{1}{316}-\frac{1}{319}\right):3\)
\(=\left(1-\frac{1}{319}\right):3\)
\(=\frac{318}{319}:3\)
\(=\frac{106}{319}\)
\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{2009.2010}=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{2009}-\frac{1}{2010}\)
\(=1-\frac{1}{2010}\)
\(=\frac{2010-1}{2010}=\frac{2019}{2010}\)
\(\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+...+\frac{2}{2009.2011}+\frac{2}{2011.2013}\)
\(=\frac{2}{3}-\frac{2}{5}+\frac{2}{5}-\frac{2}{7}+\frac{2}{7}-\frac{2}{9}+...+\frac{2}{2009}-\frac{2}{2011}+\frac{2}{2011}-\frac{2}{2013}\)
\(=\frac{2}{3}-\frac{2}{2013}\)
\(=\frac{1342-2}{2013}=\frac{1340}{2013}\)
\(\frac{1}{1.4}+\frac{1}{4.7}+\frac{1}{7.10}+...+\frac{1}{316.319}\)
\(=\left(\frac{3}{1.4}+\frac{3}{4.7}+...+\frac{3}{316.319}\right):3\)
\(=\left(3-\frac{3}{4}+\frac{3}{4}-\frac{3}{7}+\frac{3}{7}-\frac{3}{10}+...+\frac{3}{316}-\frac{3}{319}\right):3\)
\(=\left(3-\frac{3}{319}\right):3\)
\(=\frac{954}{319}:3\)
\(=\frac{318}{319}\)