Question

13 и 14 помогите пж. срочно. дам 30 баллов

Answer 1

$13)\; \; \frac{15^{n+1}\cdot 3^{n-1}}{15^{n}}=15\cdot 3^{n-1}=\frac{15\cdot 3^{n}}{3}=5\cdot 3^{n}\\\\\frac{14^{n}}{2^{n-2}\cdot 7^{n+2}}=\frac{2^{n}\cdot 7^{n}}{2^{n}\cdot 2^{-2}\cdot 7^{n}\cdot 7^{2}}=\frac{2^2}{7^2}=\frac{4}{49}\\\\14)\; \; \frac{10^{n+2}-10^{n-2}}{10^{n}}=\frac{10^{n}\cdot (10^{2}+10^{-2})}{10^{n}}=100-\frac{1}{100}=100-0,01=99,99\\\\\frac{3^{n+1}-3^{n-1}}{3^{n-2}}=\frac{3^{n}\cdot (3-3^{-1})}{3^{n}\cdot 3^{-2}}=3^2\cdot (3-\frac{1}{3})=9\cdot \frac{9-1}{3}=\frac{9\cdot 8}3}=\frac{72}{3}24$