Linexponential Series
For each positive integer \(N\) let
\( S(N) = 1 + 2 \cdot 3 + 3 \cdot 3^2 + 4 \cdot 3^3 + 5 \cdot 3^4 + \cdots + (N+1) \cdot 3^N \)
So for example \( S(1) = 1 + 6 = 7 \) and \( S(2) = 1 + 6 + 27 = 34 \).
| Part A | What are the last six digits of \(S(123)\)? | |
|---|---|---|
| Part B | What are the first six digits of \(S(123456789)\)? | |
| Part C | What are the last six digits of \(S(2021^{2021})\)? |