Question

5^n^+^1-5^n^-^1/2*5^n 10*2^n/2^n^+^1+2^n^-^1 решите

Answer 1

[$\frac{5^{n+1}-5^{n-1}}{2*5^n}=\frac{5^{n}*5-5^n*5^{-1}}{2*5^n}=\frac{5^{n}(5-5^{-1})}{2*5^n}=\frac{5-\frac15}{2}=\frac{\frac{25-1}{5}}{2}=\frac{\frac{24}{5}}{2}=\frac{24}{5}*\frac12=\\\\=\frac{12}{5}=2\frac25$

$\frac{10*2^n}{2^{n+1}+2^{n-1}}=\frac{10*2^n}{2^{n}*2+2^n*2^{-1}}=\frac{10*2^n}{2^{n}(2+2^{-1})}=\frac{10}{2+\frac12}=\frac{10}{\frac52}=10*\frac25=4$