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\(A=\frac{\frac{2}{7}+\frac{2}{5}+\frac{2}{17}-\frac{2}{293}}{\frac{3}{7}+\frac{3}{5}+\frac{3}{17}-\frac{3}{293}}\)
\(A=\frac{2.\left(\frac{1}{7}+\frac{1}{5}+\frac{1}{17}-\frac{1}{293}\right)}{3.\left(\frac{1}{7}+\frac{1}{5}+\frac{1}{17}-\frac{1}{293}\right)}\)
\(A=\frac{2}{3}\)
Ta có :\(B=\frac{3}{2}-\left(\frac{3}{2}\right)^2+\left(\frac{3}{2}\right)^3-....-\left(\frac{3}{2}\right)^{2014}\)
\(\frac{3}{2}B=\left(\frac{3}{2}\right)^2-\left(\frac{3}{2}\right)^3+\left(\frac{3}{2}\right)^4-...+\left(\frac{3}{2}\right)^{2014}-\left(\frac{3}{2}\right)^{2015}\)
\(\frac{3}{2}B+B=\left(\frac{3}{2}\right)^2-\left(\frac{3}{2}\right)^3+..+\left(\frac{3}{2}\right)^{2014}-\left(\frac{3}{2}\right)^{2015}\) \(+\frac{3}{2}-\left(\frac{3}{2}\right)^2+\left(\frac{3}{2}\right)^3-...-\left(\frac{3}{2}\right)^{2014}\)
\(\frac{5}{2}B=\frac{3}{2}-\left(\frac{3}{2}\right)^{2015}\)
\(B=\frac{\frac{3}{2}-\left(\frac{3}{2}\right)^{2015}}{\frac{5}{2}}\)
a) \(2x^2y^3.\dfrac{1}{4}xy^3\left(-3\right)xy\)
\(=\left(-3.2.\dfrac{1}{4}\right)x^4y^7\)
\(=\dfrac{-3}{2}x^4y^7\)
\(\Rightarrow Hệ\) số: \(\dfrac{-3}{2}\)
Phần biến: \(x^4y^7\)
b) \(\left(-2x^3y\right)^2.xy^2.\dfrac{1}{5}y^5\)
\(=\dfrac{4}{5}x^7y^9\)
\(\Rightarrow Phần\) biến: \(x^7y^9\)
Hệ số: \(\dfrac{4}{5}.\)
a/ \(2x^2y^3\cdot\dfrac{1}{4}xy^3\left(-3xy\right)\)
\(=\left[2\cdot\dfrac{1}{4}\cdot\left(-3\right)\right]\left(x^2.x.x\right)\left(y^3.y^3.y\right)\)
\(=-\dfrac{3}{2}x^4y^7\)
Phần biến: \(x^4y^7\)
Hệ số: \(-\dfrac{3}{2}\)
b/ \(\left(-2x^3y\right)^2\cdot xy^2\cdot\dfrac{1}{5}y^5=4x^6y^2\cdot xy^2\cdot\dfrac{1}{5}y^5\) \(=4\cdot\dfrac{1}{5}\left(x^6\cdot x\right)\left(y^2\cdot y^2\cdot y^5\right)=\dfrac{4}{5}x^7y^9\)
Phần biến: \(\dfrac{4}{5}\)
Hệ số: \(x^7y^9\)
a, 5^n +5^(n+2)
=5(5n-1+5n+1)
=26*5n
b,2/3. 3^(n-1)
=2*3n-2