simplify $$\sum_{r=1}^{2n}{(r-1)(r+1)}$$
You asked:
Simplify the expression: \(\sum_{r = 1}^{2 n} {\left(r - 1\right) \cdot \left(r + 1\right)}\)
MathBot Answer:
Simplified:
\[ \sum_{r = 1}^{2 n} {\left(r - 1\right) \cdot \left(r + 1\right)} = - \sum_{r=1}^{2 n} 1 + \sum_{r=1}^{2 n} r^{2} \]
Expanded:
\[ \sum_{r = 1}^{2 n} {\left(r - 1\right) \cdot \left(r + 1\right)} = \sum_{r=1}^{2 n} -1 + \sum_{r=1}^{2 n} r^{2} \]