In Exercises 29–42, find each indicated sum. 4Σi=1 2i^2

Verified step by step guidance

1. Identify the summation notation: \( \sum_{i=1}^{4} 2i^2 \). This means you need to calculate the sum of the expression \( 2i^2 \) as \( i \) goes from 1 to 4.
2. Substitute each integer value of \( i \) from 1 to 4 into the expression \( 2i^2 \).
3. Calculate each term: \( 2(1)^2 \), \( 2(2)^2 \), \( 2(3)^2 \), and \( 2(4)^2 \).
4. Evaluate each expression: \( 2(1)^2 = 2 \), \( 2(2)^2 = 8 \), \( 2(3)^2 = 18 \), \( 2(4)^2 = 32 \).
5. Add the results of each term together: \( 2 + 8 + 18 + 32 \).

Key Concepts

Summation Notation

Summation notation, represented by the Greek letter Sigma (Σ), is a concise way to express the sum of a sequence of terms. The notation Σ from i=a to b indicates that you sum the expression for each integer value of i starting from a up to b. In this case, 4Σi=1 means you will sum the expression 2i² for i values from 1 to 4.

Quadratic Functions

Quadratic functions are polynomial functions of degree two, typically expressed in the form f(x) = ax² + bx + c. In the context of the given problem, the term 2i² represents a quadratic function where the variable i is squared and multiplied by 2. Understanding how to evaluate quadratic expressions is essential for calculating the sum in the problem.

Evaluating Sums

Evaluating sums involves calculating the total of a series of numbers generated by a specific formula or function. In this exercise, you will compute the values of 2i² for i = 1, 2, 3, and 4, and then add these results together. Mastery of basic arithmetic operations and the order of operations is crucial for accurately performing these calculations.