Question

2^n+1 +  6^n+1=
3^n+1 + 3^2n+2

Answer 1

2^n+1 +  6^n+1=
3^n+1 + 3^2n+2

$\frac{ 2^{n+1} + 6^{n+1} }{ 3^{n+1} + 3^{n+2}}= \frac{ 2^{n+1} (1+ 3^{n+1}) }{ 3^{n+1}(1 + 3)} =(\frac{2}{3})^{n+1}* \frac{1 + 3^{n+1}}{4}$