3. $\frac{4^{n-2}}{(2^{n-1}-2^{n-2})^2}$

Question

Вопрос: $Фото задания: 3. $\frac{4^{n-2}}{(2^{n-1}-2^{n-2})^2}$$ Фото задания

Accepted Answer

$4^{n-2}=2^{2n-4}$, ал:

\[2^{n-1}-2^{n-2}=2^{n-2}(2-1)=2^{n-2}.\]

Сонда:

\[\frac{4^{n-2}}{(2^{n-1}-2^{n-2})^2}=\frac{2^{2n-4}}{(2^{n-2})^2}=\frac{2^{2n-4}}{2^{2n-4}}=1.\]

Жауабы: $1$.

3. \(\frac{4^{n-2}}{(2^{n-1}-2^{n-2})^2}\)