Đặt S=\(\frac{1}{5}+\frac{1}{5^2}+\frac{1}{5^3}+...+\frac{1}{5^{2008}}\)
5S=\(1+\frac{1}{5}+\frac{1}{5^2}+\frac{1}{5^3}+...+\frac{1}{5^{2007}}\)
5S-S=\(1+\frac{1}{5}+\frac{1}{5^2}+\frac{1}{5^3}+...+\frac{1}{5^{2007}}\)-\(\left(\frac{1}{5}+\frac{1}{5^2}+\frac{1}{5^3}+...+\frac{1}{5^{2008}}\right)\)
4S=\(1-\frac{1}{5^{2008}}\)
=> S=\(\frac{1-\frac{1}{5^{2008}}}{4}\)
tính tổng sau :\(c=\frac{\frac{1}{2008}-\frac{1}{2009}-\frac{1}{2010}}{\frac{5}{2008}-\frac{5}{2009}-\frac{5}{2010}}+\)\(\frac{\frac{2}{2007}-\frac{2}{2008}-\frac{2}{2009}}{\frac{3}{2007}-\frac{3}{2008}-\frac{3}{2009}}\)
tính:
G = \(\frac{1}{5}+\frac{1}{5^2}+\frac{1}{5^3}+...+\frac{1}{5^{2008}}\)
Tính
C= \(\frac{\frac{1}{3}-\frac{1}{5}-\frac{1}{7}}{2\frac{2}{3}-1+\frac{5}{7}}+\frac{1+\frac{4}{5}-\frac{2}{3}}{\frac{5}{4}+1-\frac{5}{6}}\)
Tính
\(P = 2018.(\frac{\frac{1}{3} - \frac{1}{5} + \frac{1}{7}}{\frac{5}{3} - 1 +\frac{5}{7}} + \frac{1 +\frac{4}{5} -\frac{2}{3}}{\frac{5}{4} + 1 -\frac{5}{6}}) : \frac{20182018}{20192019}\)
Bài 1:Tính
\(\frac{\frac{1}{3}-\frac{4}{5}}{\frac{1}{3}+\frac{4}{5}}.\frac{\frac{3}{4}-\frac{5}{3}}{\frac{3}{4}+\frac{5}{3}}:\frac{\frac{4}{5}-1}{1-\frac{2}{3}}\)
Tính \(\frac{1}{2}-\frac{1}{3}-\frac{2}{3}+\frac{1}{4}+\frac{2}{4}+\frac{3}{4}-\frac{1}{5}-\frac{2}{5}-\frac{3}{5}-\frac{4}{5}+...+\frac{1}{10}+...+\frac{9}{10}\)
Tìm x
n)\(\frac{x+1}{2008}=\frac{502}{x+1}\)
p) \(\left|\frac{5}{4}x-\frac{7}{2}\right|-\left|\frac{5}{8}x+\frac{3}{5}\right|=0\)
Tính \(A=\frac{\frac{3}{4}-\frac{3}{11}+\frac{3}{13}}{\frac{5}{7}-\frac{5}{11}+\frac{5}{13}}+\frac{\frac{1}{2}-\frac{1}{3}+\frac{1}{4}}{\frac{5}{4}-\frac{5}{6}+\frac{5}{8}}\)
Tính hợp lý \(\frac{\frac{2}{5}+\frac{2}{7}-\frac{2}{11}}{\frac{3}{5}+\frac{3}{7}-\frac{3}{11}}+\frac{\frac{1}{4}-\frac{1}{5}+\frac{1}{7}}{\frac{3}{4}-\frac{3}{5}+\frac{3}{7}}\)
