Find the value of the summation. \[ \sum_{k=1}^{4}\left(k^{2}-2\right)= \]

Step 1 ：The given expression is a summation of a series from k=1 to 4. The series is of the form \(k^{2} - 2\). To find the value of the summation, we need to substitute each value of k from 1 to 4 into the expression and add the results together.

Step 2 ：Substitute k=1 into the expression, we get \(1^{2} - 2 = -1\)

Step 3 ：Substitute k=2 into the expression, we get \(2^{2} - 2 = 2\)

Step 4 ：Substitute k=3 into the expression, we get \(3^{2} - 2 = 7\)

Step 5 ：Substitute k=4 into the expression, we get \(4^{2} - 2 = 14\)

Step 6 ：Add all the results together, we get \(-1 + 2 + 7 + 14 = 22\)

Step 7 ：So, the value of the summation is \(\boxed{22}\)