\(\frac{1}{1.2}+\frac{1}{2.3}+....+\frac{1}{x\left(x+1\right)}=\frac{2009}{2010}\)
\(\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-....-\frac{1}{x}+\frac{1}{x}-\frac{1}{\left(x+1\right)}=\frac{2009}{2010}\)
\(1-\frac{1}{x+1}=\frac{2009}{2010}\)
\(\frac{1}{x+1}=1-\frac{2009}{2010}=\frac{1}{2010}\)
\(\Leftrightarrow\) x + 1= 2010
< = > x = 2010 - 1 = 2009
Tìm số tự nhiên x biết:
\(\left(\frac{1}{1\cdot2\cdot3}+\frac{1}{2\cdot3\cdot4}+...+\frac{1}{8\cdot9\cdot10}\right)\cdot x=\frac{23}{45}\)
Tìm số tự nhiên x, biết: \(\left(\frac{1}{1\cdot2\cdot3}+\frac{1}{2\cdot3\cdot4}+...+\frac{1}{8\cdot9\cdot10}\right)\cdot x=\frac{23}{45}\)
Tìm x biết : \(\left(\frac{1}{1\cdot2}+\frac{1}{1\cdot3}+\frac{1}{3\cdot4}+...+\frac{1}{99.100}\right)-2\cdot x=\frac{1}{2}\).
Các bạn giúp mình với .
Tìm x, biết :
a, \(\left(\frac{1}{1\cdot2\cdot3}+\frac{1}{2\cdot3\cdot4}+...+\frac{1}{98\cdot99\cdot100}\right)x=-3\);
b, \(\left(\frac{\frac{2000}{1}+\frac{1999}{2}+...+\frac{1}{2000}}{\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2001}}\right)x=\frac{-1}{5}\).
c,\(\left(\frac{\frac{2000}{1}+\frac{1999}{2}+...+\frac{1}{2000}+2000}{1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2001}}\right):x=\frac{-2001}{2002}\).
Tìm x,biết
a)(x+1)+(x+2)+........+(x+100)=5750
b)\(\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+........+\frac{1}{x\cdot\left(x+1\right)}=\frac{2015}{2016}\)
c)\(\frac{1}{21}+\frac{1}{28}+\frac{1}{36}+..........+\frac{2}{x\cdot\left(x+1\right)}=\frac{2}{9}\)
Bài 1:Tìm x
\(\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+...+\frac{1}{x\cdot\left(x+1\right)}=\frac{215}{216}\)
giúp mình cách trình bày với nhé mai phải nộp rồi
Tính tổng :
a) \(A=\frac{5}{2\cdot1}+\frac{4}{1\cdot11}+\frac{3}{11\cdot14}+\frac{1}{14\cdot15}+\frac{13}{15\cdot28}\)
b) \(B=\frac{-1}{20}+\frac{-1}{30}+\frac{-1}{42}+\frac{-1}{56}+\frac{-1}{72}+\frac{-1}{90}\)
c) \(C=\frac{1}{1\cdot2\cdot3}+\frac{1}{2\cdot3\cdot4}+...+\frac{1}{n\left(n+1\right)\left(n+2\right)}\)
d) \(D=\frac{1}{1\cdot2\cdot3\cdot4}+\frac{1}{2\cdot3\cdot4\cdot5}+...+\frac{1}{n\left(n+1\right)\left(n+2\right)\left(n+3\right)}\)
e) \(E=\left(\frac{1}{1\cdot2\cdot3}+\frac{1}{2\cdot3\cdot4}+...+\frac{1}{37\cdot38\cdot39}\right)\cdot1482\cdot185\cdot8\)
tìm x biết
1)\(-\frac{2}{3}\cdot\left(x-\frac{1}{4}\right)=\frac{1}{3}\cdot\left(2x-1\right)\)
2)\(\frac{1}{5}\cdot2^x+\frac{1}{5}\cdot2^{x+1}=\frac{1}{5}\cdot2^7+\frac{1}{3}\cdot2^8\)
Tìm x, biết:
\(\left(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2008}\right).x=\frac{2009}{1}+\frac{2010}{2}+\frac{2011}{3}+...+\frac{4016}{2008}-2008\)
