Question

Tính : 

\(\dfrac{25^5+25^7+25^9}{5^{11}+5^{13}+5^{15}+5^{17}+5^{19}+5^{21}}\)

Answer 1

\(\dfrac{25^5+25^7+25^9}{5^{11}+5^{13}+5^{15}+5^{17}+5^{19}+5^{21}}\)

\(=\dfrac{5^{10}+5^{14}+5^{18}}{5^{11}+5^{13}+5^{17}+5^{19}+5^{21}}\)

\(=\dfrac{5^{10}\left(1+5^4+5^8\right)}{5^{11}\left(1+5^2+5^4+5^6+5^8+5^{10}\right)}\)

\(=\dfrac{1+5^4+5^8}{5+5^3+5^5+5^7+5^9+5^{11}}\)

\(=\dfrac{1+5^4+5^8}{\left(5+5^5+5^9\right)+\left(5^3+5^7+5^{11}\right)}\)

\(=\dfrac{1+5^4+5^8}{\left(1+5^4+5^8\right)\left(5+5^3\right)}\)

\(=\dfrac{1}{5+5^3}\)

\(=\dfrac{1}{130}\)

\(\)