Solving a series $n(1 + n + n^2 + n^3 + n^4 +.......n^{n-1})$ I'm trying to sum the following series?

$n(1 + n + n^2 + n^3 + n^4 +.......n^{n-1})$

Do you have any ideas?

Let $ n + n^2 + n^3 + n^4 + \cdot\cdot\cdot + n^n = Sum $
 Then, 
 $ 1 + n + n^2 + n^3 + n^4 + \cdot\cdot\cdot + n^n  = Sum + 1$
 $ n \times (1 + n + n^2 + n^3 + n^4 + \cdot\cdot\cdot + n^n ) = n \times (Sum + 1)$
 $ n + n^2 + n^3 + n^4 + \cdot\cdot\cdot + n^n + n^{n+1} = n\times Sum + n$
 $ (n + n^2 + n^3 + n^4 + \cdot\cdot\cdot + n^n) + n^{n+1} = n\times Sum + n$
 $ (Sum)+ n^{n+1} = n\times Sum + n$
 $ n^{n+1} = (n-1) \times Sum + n$
 $ n^{n+1} -n = (n-1) \times Sum$
 $ \frac {n^{n+1} -n}{n-1} = Sum$
Hence,
      $ Sum = \sum_{i = 1}^{n} n^i = \frac {n^{n+1} -n}{n-1} $
