The sum of given series is 44
Solution:
Given that we have to find the sum of the series
Given series is:
[tex]\sum_{k=1}^{4}\left(2 k^{2}-4\right)[/tex]
Substitute k = 1 to k = 4 to find the sum of the series
When k = 1:
[tex]\rightarrow 2(1)^2 - 4 = 2 - 4 = -2[/tex]
When k = 2:
[tex]\rightarrow 2(2)^2 - 4 = 2(4) - 4 = 8 - 4 = 4[/tex]
When k = 3:
[tex]\rightarrow 2(3)^2 - 4 = 2(9) - 4 = 18 - 4 = 14[/tex]
When k = 4:
[tex]\rightarrow 2(4)^2 - 4 = 2(16) - 4 = 32 - 4 = 28[/tex]
Therefore, the sum of series is given as:
[tex]\sum_{k=1}^{4}\left(2 k^{2}-4\right)=-2+4+14+28=44[/tex]
Thus the sum of series is 44
