Question

Apply the properties of exponents to verify that each statement is an identity

.(3^n+1) − 3^n =( 2 ∙ 3^n) for integer values of n

Answer 1

Answer and explanation :

We have given expression
`3^(n+1)-3^n=2* 3^n` for integer value of n

We have to prove L.H.S = R.H.S

Lets take L.H.S

`3^(n+1)-3^n`

`3^(n+1)` can be written as
`3^n.3`

So
`3^n.3-3^n`

Now take
`3^n` as common

`3^n(3-1)=2.3^n` = R.H.S

Hence proved