Show that:
\[1*3+2*3^{2}+...+n3^{n} =\frac{ (2n-1)3^{n+1}+1 }{ 4 }\]
for every number n where \[n \in \mathbb{N}, \mathbb{N}>0\]
If you try the induction formula with n=2,3 it get's wrong so is it the right conclution to just say that it isn't correct for all positive n ?

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PMI will do it..)

p(1) = 3
p(k) =
\[\frac{ (2k-1)3^{k+1} +1}{ 4 }\]

We shuld Prove
p(k+1) =
\[\frac{ (2(k+1)-1)3^{k+1+1} +1}{ 4 }\]

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