Question

What is the sum of the series?

Answer 1

The sum of given series is 44

Solution:

Given that we have to find the sum of the series

Given series is:

`\sum_(k=1)^(4)\left(2 k^(2)-4\right)`

Substitute k = 1 to k = 4 to find the sum of the series

When k = 1:

`\rightarrow 2(1)^2 - 4 = 2 - 4 = -2`

When k = 2:

`\rightarrow 2(2)^2 - 4 = 2(4) - 4 = 8 - 4 = 4`

When k = 3:

`\rightarrow 2(3)^2 - 4 = 2(9) - 4 = 18 - 4 = 14`

When k = 4:

`\rightarrow 2(4)^2 - 4 = 2(16) - 4 = 32 - 4 = 28`

Therefore, the sum of series is given as:

`\sum_(k=1)^(4)\left(2 k^(2)-4\right)=-2+4+14+28=44`

Thus the sum of series is 44