Question

Решите : 325*20^n / 4^n +4^n+1

Answer 1

$\frac{325\cdot 20^{n}}{4^{n}+4^{n+1}} =\frac{13\cdot 5^2\cdot (5^{n}\cdot 4^{n})}{4^{n}\cdot (1+4)} =\frac{13\cdot 5^2\cdot 5^{n}\cdot 4^{n}}{4^{n}\cdot 5} = \frac{13\cdot 5\cdot 5^{n}}{1\cdot 1} =65\cdot 5^{n}\\\\ili\; \; \; \; 13\cdot 5\cdot 5^{n}=13\cdot 5^{n+1}$