Answer and explanation :
We have given that the expression [tex]\frac{2^{n+1}}{3^n}=2\times (\frac{2}{3})^n[/tex]
We have to prove L.H.S = R.H.S
Lets take L.H.S
[tex]\frac{2^{n+1}}{3^n}[/tex]
It can be written as [tex]\frac{2^{n+1}}{3^n}=\frac{2^n\times 2^1}{3^n}[/tex] ( As in multiplication exponent are added )
So [tex]\frac{2^n\times 2^1}{3^n}=(\frac{2}{3})^n\times 2[/tex] = R.H.S
Hence proved
