Question

( 5 * ( 25 ) ^ ( n + 1 ) - 25 * ( 5 ) ^ ( 2 n ) )/( 5 * ( 5 ) ^ ( 2 n + 3 ) - ( 25 ) ^ ( n + 1 ) )

Answer 1

now that is your ans

Answer 2

Answer:

$\frac{1}{6}$

Step-by-step explanation:

Given expression is,

$\frac{5\times (25)^{n+1} - 25(5)^{2n}}{5\times 5^{2n+3}-(25)^{n+1}}$

$=\frac{5(25)^{n+1} - 25(5^2)^{n}}{5^{1+2n+3}-(25)^{n+1}}$ ( Since, $a^{mn}=(a^m)^n$ and $a^m.a^n=a^{m+n}$ )

$=\frac{5(25)^{n+1} - 25(25)^{n}}{5^{2n+4}-(25)^{n+1}}$

$=\frac{5(25)^{n+1} - (25)^{n+1}}{(5^2)^{n+2}-(25)^{n+1}}$

$=\frac{5(25)^{n+1} - (25)^{n+1}}{(25)^{n+2}-(25)^{n+1}}$

$=\frac{(25)^{n+1}(5-1)}{(25)^{n+1}(25-1)}$

$=\frac{4}{24}$

$=\frac{1}{6}$