Question 10
If $$S = 4^2 + 2 \cdot 5^2 + 3 \cdot 6^2 + \ldots + 25 \cdot 28^2$$, then the value of $$\frac{S}{325}$$ is equal to
Solution
The general term is $$n(n+3)^2 = n^3 + 6n^2 + 9n$$ for $$n$$ from 1 to 25. Using $$\sum n^3 = 105625$$, $$\sum n^2 = 5525$$ and $$\sum n = 325$$, we get $$S = 105625 + 6(5525) + 9(325) = 141700$$. Hence $$\frac{S}{325} = 436$$.
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