Using PMI prove un=((-1)^(n+1))/3 + (2^n)/3

[AerospaceEng]

Solved thank you.

Thank you for all the help just a little forgetful mistake.

 

[micromass]

You didn't use the induction hypothesis yet. You need to sub

$$u_n = \frac{(-1)^{n+1}+2^n}{3}$$

and

$$u_{n-1} = \frac{(-1)^n+2^{n-1}}{3}$$