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Question
If \[\sum^n_{r = 1} r = 55, \text{ find } \sum^n_{r = 1} r^3\] .
Solution
\[\sum^n_{r = 1} r^3 = 1^3 + 2^3 + 3^3 + . . . + n^3 \]
\[ = \left[ \frac{n\left( n + 1 \right)}{2} \right]^2 \]
\[ = \left[ \sum^n_{r = 1} r \right]^2 \]
\[ = \left[ 55 \right]^2 \]
\[ = 3025\]
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