Question

Сократите дробь 4^n+1 - 4^n-1/4^n-2

Answer 1

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

$=4^{n-(n-2)} * \frac{15}{4} =4^{n-n+2} * \frac{15}{4} =4^2*\frac{15}{4}=60$