\(9^x.3^7=3^{x-1}\)

\(\Leftrightarrow\left(3^2\right)^x.3^7=3^{x-1}\)

\(\Leftrightarrow3^{2x}.3^7=3^{x-1}\)

\(\Leftrightarrow3^{2x+7}=3^{x-1}\)

\(\Leftrightarrow2x+7=x-1\)

\(\Leftrightarrow x-1-2x=7\)

\(\Leftrightarrow-x-1=7\)

\(\Leftrightarrow-x=8\) 

\(\Leftrightarrow x=-8\)

Giúp với, t cho 3 k =.=

\(S2=\left(\frac{1}{3}-\frac{1}{1001}\right):2=\frac{499}{3003}\)

\(S2=\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{999.1001}\)

\(S2=\frac{1}{2}\left(\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{999.1001}\right)\)

\(S2=\frac{1}{2}\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{999}-\frac{1}{1001}\right)\)

\(S2=\frac{1}{2}\left(\frac{1}{3}-\frac{1}{1001}\right)\)

\(S2=\frac{1}{2}.\frac{998}{3003}=\frac{499}{3003}\)

\(\left(1-\frac{1}{2^2}\right).\left(1-\frac{1}{3^2}\right).\left(1-\frac{1}{4^2}\right)...\left(1-\frac{1}{n^2}\right)\)

\(=\frac{3}{2^2}.\frac{8}{3^2}.\frac{15}{4^2}...\frac{\left(n-1\right).\left(n+1\right)}{n^2}\)

\(=\frac{1.3}{2.2}.\frac{2.4}{3.3}.\frac{3.5}{4.4}...\frac{\left(n-1\right).\left(n+1\right)}{n.n}\)

\(=\frac{1.2.3...\left(n-1\right)}{2.3.4...n}.\frac{3.4.5...\left(n+1\right)}{2.3.4...n}\)

\(=\frac{1}{n}.\frac{n+1}{2}=\frac{n+1}{2n}\)