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đặt a=1/3+1/6+1/10+...........+2/n(n+1)
1/2a=1/6+1/12+...........+1/n(n+1)
1/2a=1/2.3+1/3.4+........+1/n(n+1)
1/2a=1/2-1/3+1/3-1/4+.......+1/n-1/n+1
1/2a=1/2-1/n+1
a=(1/2--1/n+1):1/2=2003/2004
1/2-1/n+1=2003/2004.1/2
1/2-1/n+1=2003/4008
1/n+1=1/2-2003/4008
1/n+1=1/4008
suy ra n+1=4008
n=4007
\(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+\frac{2}{n\left(n+1\right)}\)
\(=\frac{2}{6}+\frac{2}{12}+\frac{2}{20}+...+\frac{2}{n\left(n+1\right)}\)
\(=\frac{2}{2.3}+\frac{2}{3.4}+\frac{2}{4.5}+...+\frac{2}{n\left(n+1\right)}\)
\(=2\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{n}-\frac{1}{n+1}\right)\)
\(=2\left(\frac{1}{2}-\frac{1}{n+1}\right)=\frac{2010}{2011}\)
\(\Leftrightarrow n=4021\).
a, \(\frac{64}{2^n}=16\Leftrightarrow\frac{64}{2^n}=\frac{64}{4}\Leftrightarrow2^n=4\Leftrightarrow n=2\)
b, \(\left(\frac{1}{3}\right)^{2n-1}=\left(\frac{1}{3}\right)^3\Leftrightarrow2n-1=3\Leftrightarrow n=2\)
a)\(\frac{64}{2^n}=16\Leftrightarrow2^n.16=64\Leftrightarrow2^n=4\Leftrightarrow2^n=2^2\Leftrightarrow n=2\)
b)\(\left(\frac{1}{3}\right)^{2n-1}=\frac{1}{27}\)
\(\Leftrightarrow\left(\frac{1}{3}\right)^{2n-1}=\left(\frac{1}{3}\right)^3\)
\(\Leftrightarrow2n-1=3\Leftrightarrow2n=4\Leftrightarrow n=2\)