Question

{5^(n+2)-5^(n+1)}/{5^(n+3)​

Answer 1

$\rm \dfrac{5^{n+2}-5^{n+1}}{5^{n+3}}$

_________________________________

$\rm \implies\dfrac{5^{n+2}-5^{n+1}}{5^{n+3}}$

$\rm \implies\dfrac{5^{n} \times 5^2-5^{n} \times 5}{5^{n} \times 5^3}\qquad\qquad ...[ since, \ a^{m+n} = a^m \times a^n]$

$\rm Let \ 5^n = a$

$\rm \implies\dfrac{a \times 5^2-a \times 5}{a \times 5^3}$

$\rm \implies\dfrac{a \times 25-a \times 5}{a \times 125}$

$\rm \implies\dfrac{25a-5a}{125a}$

$\rm \implies\dfrac{20a}{125a}$

$\rm \implies\dfrac{4a}{25a}$

a will get cancelled.

$\rm \implies\dfrac{4}{25}$

Answer:- 4/25

Hope it helps...