Question

What is the sum of the series? 4 ∑k=1 (2k^2−4)

Answer 1

The sum of the series $\sum_{k=1}^{4}\left(2 k^{2}-4\right)$ is 44.

Step-by-step explanation:

The given series is $\sum_{k=1}^{4}\left(2 k^{2}-4\right)=44$

To find the sum of the series, we need to substitute the values for k in the series.

$\sum_{k=1}^{4}\left(2 k^{2}-4\right)=\left[2(1)^{2}-4\right]+\left[2(2)^{2}-4\right]+\left[2(3)^{2}-4\right]+\left[2(4)^{2}-4\right]$

Now, simplifying the square terms, we get,

$[2(1)-4]+[2(4)-4]+[2(9)-4]+[2(16)-4]$

Multiplying the terms,

$[2-4]+[8-4]+[18-4]+[32-4]$

Subtracting the values within the bracket term, we get,

$-2+4+14+28$

Now, adding all the terms, we get the sum of the series,

$\sum_{k=1}^{4}\left(2 k^{2}-4\right)=44$

Thus, the sum of the series is $\sum_{k=1}^{4}\left(2 k^{2}-4\right)=44$