Dear Student 5×25n+1- 25×52n5×52n+3- 25n+1 =5×52n+2- 52×52n52n+4- 52n+2⇒52n+3- 52n+252n+4- 52n+2=52n+25-152n+225-1=424=16 Regards

Solve the sum.

Dear Student

\frac{5 \times {(25)}^{n + 1} - 25 \times 5^{2 n}}{5 \times {(5)}^{(2 n + 3)} - {(25)}^{n + 1}} = \frac{5 \times {(5)}^{2 n + 2} - 5^{2} \times 5^{2 n}}{{(5)}^{(2 n + 4)} - {(5)}^{2 n + 2}} \Rightarrow \frac{{(5)}^{2 n + 3} - 5^{2 n + 2}}{{(5)}^{(2 n + 4)} - {(5)}^{2 n + 2}} = \frac{5^{2 n + 2} (5 - 1)}{5^{2 n + 2} (25 - 1)} = \frac{4}{24} = \frac{1}{6}

Regards