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Apply the properties of exponents to verify that each statement is an identit.
(.2^n+1)/3^n =2 ( 2/3)^n for integer values of n

Respuesta :

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  

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