Question

In Exercises \(1-6,\) find the sum. Use the summation capabilities of a graphing utility to verify your result. $$ \sum_{k=3}^{6} k(k-2) $$

Short answer

The sum of the series \(\sum_{k=3}^{6} k(k-2)\) is 50.

Step-by-step solution

Evaluate the function for each value of \(k\)

Substitute the integers from 3 up to 6 inclusive into the function \(k(k-2)\):For \(k=3\), \(k(k-2)=3(3-2)=3\);For \(k=4\), \(k(k-2)=4(4-2)=8\);For \(k=5\), \(k(k-2)=5(5-2)=15\);For \(k=6\), \(k(k-2)=6(6-2)=24.

Sum up the values obtained

Add up the values obtained from substituting each respective \(k\) in Step 1: \(3+8+15+24=50\).