evaluate $$\sum_{r=1}^{2n}{(r-1)(r+1)}$$
You asked:
Evaluate the expression: \(\sum_{r = 1}^{2 n} {\left(r - 1\right) \cdot \left(r + 1\right)}\)
MathBot Answer:
Evaluated
\(\displaystyle \sum_{r = 1}^{2 n} {\left(r - 1\right) \cdot \left(r + 1\right)} = \frac{8 n^{3}}{3} + 2 n^{2} - \frac{5 n}{3} \)
Expanded
\[\sum_{r = 1}^{2 n} {\left(r - 1\right) \cdot \left(r + 1\right)} = \sum_{r=1}^{2 n} -1 + \sum_{r=1}^{2 n} r^{2}\]