Problem 31 - College Algebra

Question

Find each indicated sum. $$\sum_{i=1}^{4} 2 i^{2}$$

Step-by-Step Solution

Answer

The sum of the series, \(\sum_{i=1}^{4} 2 i^{2}\) is 60.

Step 1: Understand the notation

The given notation, \(\sum_{i=1}^{4} 2 i^{2}\), represents a series sum from 'i' equals 1 to 4. The summand, or individual term in the series, is \(2i^2\). Thus for each 'i' from 1 to 4, the term \(2i^2\) is to be calculated and then all these computed terms are added together to obtain the sum.

Step 2: Compute each term

First, calculate each term in the series for 'i' from 1 to 4. They are: \(2*1^2 = 2\), \(2*2^2 = 8\), \(2*3^2 = 18\), and \(2*4^2 = 32\).

Step 3: Sum the terms

Now, sum these calculated terms. The sum is: \(2 + 8 + 18 + 32 = 60\).