Write each series as a summation in sigma notation.

(−1)^2+0^2+1^2+2^2+3^2

3

∑ k^2
k = -1

To write the given series as a summation in sigma notation, we need to understand the pattern within the series and express it using mathematical notation.

The given series is: (-1)^2 + 0^2 + 1^2 + 2^2 + 3^2

We can observe that the terms in this series are the squares of consecutive integers, starting from -1. We can express this pattern using sigma notation.

In sigma notation, the summation of a series is represented by the Greek letter sigma (Σ), followed by the expression for the terms, the starting value, and the ending value.

To write this series as a summation in sigma notation, we need to identify the expression that represents the terms in the series. In this case, the expression is the square of consecutive integers.

Let's break it down step-by-step:

1. The expression for the terms is (n)^2, where 'n' represents the consecutive integers.
2. The starting value of the series is -1, so we start from n = -1.
3. The ending value of the series is 3, so the sum goes up to n = 3.

Putting it all together, the sigma notation for the given series is:

Σ(n^2), where n = -1 to 3