1+1/3+1/6+1/10+...+1/x.(x+1):2=1+2009/2011
=>2/6+2/12+2/20+...+2/x.(x+1)=2009/2011
=>2.(1/2.3+1/3.4+1/4.5+...+1/x.(x+1))=2009/2011
=>1/2-1/3+1/3-1/4+1/4-1/5+...+1/x-1/x+1=2009/2011:2
=>1/2-1/x+1=2009/4022
=>1/x+1=1/2-2009/4022
=>1/x+1=1/2001
=.x+1=2001
=>x=2001-1
=>x=2000
vậy x=2000
tìm x, y thỏa mãn
a, \(1+\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+....+\frac{1}{x.\left(x+2\right):2}=1\frac{2009}{2011}\)
Tìm x biết: \(1+\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{1}{x\left(x+2\right):2}=\)\(1\frac{2009}{2011}\)
\(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{1}{x.\left(x+1\right):2}=\frac{2009}{2011}\)
Tìm x biết \(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{1}{x\left(x+1\right):2}=\frac{2009}{2011}\)
a) Tìm số nguyên dương x :
(x-3)+(x-2)+(x-1)+...+9+10+2011=2011
b) Tìm số tự nhiên x :
\(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{2}{n\left(n+1\right)}\)
Tim x thuoc Z, biet: \(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{1}{x\left(x+1\right):2}=\frac{2009}{2011}\)
Tìm x thoả mãn:
a)\(\frac{1}{2}x-\frac{3}{4}x-\frac{7}{3}=-\frac{5}{6}\)
b)\(\frac{4}{5}x-x-\frac{3}{2}x+\frac{4}{3}=\frac{1}{2}-\frac{6}{5}\)
c)\(\frac{1}{1.2}+\frac{1}{2.3}+......+\frac{1}{x.\left(x+1\right)}=\frac{2009}{2010}\)
d)\(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{2}{x\left(x+1\right)}=1\frac{2013}{2015}\)
e)\(\frac{1}{3.5}+\frac{1}{5.7}+.....+\frac{1}{\left(2x+1\right)\left(2x+3\right)}=\frac{100}{609}\)
3. Tìm x biết :
\(\frac{x-1}{2011}+\frac{x-2}{2010}+\frac{x-3}{2009}=\frac{x-4}{2008}\)
2. Tìm x nguyên biết :
\(1-3+3^2-3^3+...+\left(-3\right)^x=\frac{9^{1006}-1}{4}\)
\(1+\frac{1}{3}+\frac{1}{6}+...+\frac{1}{x+\left(x+2\right):2}=1\frac{2009}{2011}\)
