Tìm: \(\frac{x}{2}+\frac{x}{2.3}+\frac{x}{3.4}+...+\frac{x}{2015.2016}=\frac{2015}{4032}\)
Tính: \(\left(\frac{7}{1.2}+\frac{7}{2.3}+\frac{7}{3.4}+...+\frac{7}{2015.2016}\right):\frac{2015}{2016}\)
\(\left(\frac{7}{1.2}+\frac{7}{2.3}+\frac{7}{3.4}+...+\frac{7}{2015.2016}\right):\frac{2015}{2016}\)
=\(7\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{2015.2016}\right):\frac{2015}{2016}\)
=\(7\left(\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{2015}-\frac{1}{2016}\right):\frac{2015}{2016}\)
=\(7\left(\frac{1}{1}-\frac{1}{2016}\right):\frac{2015}{2016}=7.\frac{2015}{2016}:\frac{2015}{2016}=7\)
\(\left(\frac{7}{1\cdot2}+\frac{7}{2\cdot3}+\frac{7}{3\cdot4}+...+\frac{7}{2015\cdot2016}\right):\frac{2015}{2016}\)
\(=\left(7-\frac{7}{2}+\frac{7}{2}-\frac{7}{3}+\frac{7}{3}-\frac{7}{4}+...+\frac{7}{2015}-\frac{7}{2016}\right):\frac{2015}{2016}\)
\(=\left(7-\frac{7}{2016}\right):\frac{2015}{2016}=\frac{2015}{288}:\frac{2015}{2016}=\frac{2015}{288}\cdot\frac{2016}{2015}=\frac{2016}{288}=7\)
Giá trị của x thỏa mãn phương trình:
\(\frac{2}{1.2}+\frac{2}{2.3}+\frac{2}{3.4}+.....+\frac{2}{x\left(x+1\right)}=1\frac{2013}{2015}\) là :
\(\frac{2}{1.2}+\frac{2}{2.3}+..........+\frac{2}{x\left(x+1\right)}=1\frac{2013}{2015}\)
\(\Rightarrow2\left(\frac{1}{1.2}+\frac{1}{2.3}+........+\frac{1}{x\left(x+1\right)}\right)=\frac{4028}{2015}\)
\(\Rightarrow1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+..........+\frac{1}{x}-\frac{1}{x+1}=\frac{4028}{2015}:2\)
\(\Rightarrow1-\frac{1}{x+1}=\frac{2014}{2015}\)
\(\Rightarrow\frac{1}{x+1}=1-\frac{2014}{2015}\)
\(\Rightarrow\frac{1}{x+1}=\frac{1}{2015}\)
\(\Rightarrow x+1=2015\Rightarrow x=2014\)
\(\frac{2}{1\times2}+\frac{2}{2\times3}+\frac{2}{3\times4}+...+\frac{2}{x\left(x+1\right)}=1\frac{2013}{2015}\)
\(2\times\left(\frac{1}{1\times2}+\frac{1}{2\times3}+\frac{1}{3\times4}+...+\frac{1}{x\times\left(x+1\right)}\right)=1\frac{2013}{2015}\)
\(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{x}-\frac{1}{x+1}=1\frac{2013}{2015}\div2\)
\(1-\frac{1}{x+1}=\frac{2014}{2015}\)
\(\frac{1}{x+1}=1-\frac{2014}{2015}\)
\(\frac{1}{x+1}=\frac{1}{2015}\)
\(x+1=2015\)
\(x=2015-1\)
\(x=2014\)
Ta thấy A gồm có 99 số hạng nên ta nhóm mỗi nhóm 3 số hạng.
Ta có: A = 1 + 5 + 52 + 53 + 54 + 55 +...+ 597 + 598 + 599
= (1 + 5 + 52 )+ (53 + 54 + 55 )+...+( 597 + 598 + 599 )
=(1 + 5 + 52 )+ 53(1 + 5 + 52 ) +...+ 597(1 + 5 + 52 )
= ( 1 + 5 + 52)(1 + 53+....+597)
= 31(1 + 53+....+597)
Vì có một thừa số là 31 nên A chia hết cho 31.
P/s Đừng để ý câu trả lời của mình
giá trị của x thỏa mãn phương trình
\(\frac{2}{1.2}+\frac{2}{2.3}+\frac{2}{3.4}+...+\frac{2}{x.\left(x+1\right)}=1\frac{2013}{2015}\)là.....
Tìm x
\(\frac{x-2017}{2015.2016}+\frac{x-2018}{2016.2017}+\frac{x-2019}{2017.2018}+\frac{x-2020}{2018.1019}=\frac{1}{2015}+\frac{1}{2016}+\frac{1}{2017}+\frac{1}{1018}\)
Tìm x:
a) \(\frac{1}{3}\). x +\(\frac{2}{5}\). (x-1) =4
b)3\(^{x-1}\) + \(\frac{5}{2}\). 3\(^x\)=162
Tính :
1.2+2.3+3.4+...+2015.2016
Các bạn làm nhanh nha mai cô giáo mk kiểm tra òi
tìm x:
\(\frac{x}{1.2}+\frac{x}{2.3}+\frac{x}{3.4}...+\frac{x}{2017.2018}\)
Mk nghi~ bn ne^n xem La.i de^` nhe'
à, minh ghi thiếu.
=-1
\(\frac{x}{1.2}+\frac{x}{2.3}+\frac{x}{3.4}+...+\frac{x}{1999.2000}\) =1. Tìm x
\(\Leftrightarrow x.\left(\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{1999}-\frac{1}{2000}\right)=1\)
\(\Leftrightarrow x.\left(1-\frac{1}{2000}\right)=1\Leftrightarrow x\cdot\frac{1999}{2000}=1\Leftrightarrow x=\frac{2000}{1999}\)
Tìm x biết
\(\frac{2}{2.3}+\frac{2}{3.4}+\frac{2}{4.5}+...+\frac{2}{x.\left(x+1\right)}=\frac{2007}{2009}\)
Tìm x biết \(\frac{x}{1.2}+\frac{x}{2.3}+\frac{x}{3.4}+...+\frac{x}{2006.2007}=\frac{2006}{2007}\)
\(\frac{x}{1.2}+\frac{x}{2.3}+\frac{x}{3.4}+...+\frac{x}{2006.2007}=\frac{2006}{2007}\)
\(\frac{x}{1}-\frac{x}{2}+\frac{x}{2}-\frac{x}{3}+\frac{x}{3}-\frac{x}{4}+...+\frac{x}{2006}-\frac{x}{2007}=\frac{2006}{2007}\)
\(x-\frac{x}{2007}=\frac{2006}{2007}\)
\(\frac{2007x}{2007}-\frac{x}{2007}=\frac{2006}{2007}\)
\(2007x-x=2006\)
\(2006x=2006\)
\(x=1\)
theo suy luận của mình thì x sẽ bằng 1