Slow morning. Can someone help me figure it out? I have a feeling it is trivially easy and not worthy of a thread. $ 3^{n+1} + 3^n = 4\cdot3^n $
Thanks.
Slow morning. Can someone help me figure it out? I have a feeling it is trivially easy and not worthy of a thread. $ 3^{n+1} + 3^n = 4\cdot3^n $
Thanks.
Answers this version of the question
The previous version of the question claimed that for all $n \in \Bbb N$, $3^{n+1}+3n=4\cdot 3n \tag{1}$
However $(1)$ is not true for all $n$ as noted in the next part of the answer.
However what is true is: $3^{n+1}+3^n=4\cdot3^n$
To see this, note that $3^{n+1}=3^n \cdot 3$ and factor the $3^n$ out.
Answers the previous version of the question
Your claim is simply not true. For $n=2$, LHS equals $ 33$ while RHS evaluates to $24$.
Hint: Write $3^{n+1}$ as $3\cdot 3^n$, then factor $3^n$ out of the sum.
(I assume the question is about $3^{n+1}+3^n$.)