$$\sum_{i=1}^{n}{5(-1)^n(n-5)}$$
You asked:
Evaluate the expression: \(\sum_{i = 1}^{n} {5 \cdot {\left( -1 \right)}^{n \cdot \left(n - 5\right)}}\)
MathBot Answer:
\[\sum_{i=1}^{n} 5 \left(-1\right)^{n \left(n - 5\right)} = 5 \left(-1\right)^{n \left(n - 5\right)} n\]