Question

Evaluate:
5*[25^n+1] - 25 * (5^2n) / 5 * (5^2n+3) - (25^n+1)

Answer 1

Step-by-step explanation:

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