Sigma notation Express the following sums using sigma notation. (Answers are not unique.)
(b) 4 + 5 + 6 + 7 + 8 + 9

Verified step by step guidance

1. Step 1: Understand the problem. The goal is to express the sum 4 + 5 + 6 + 7 + 8 + 9 using sigma notation, which is a compact way to represent summation.
2. Step 2: Identify the pattern in the sequence. The numbers in the sum are consecutive integers starting from 4 and ending at 9.
3. Step 3: Define the general term of the sequence. The general term can be written as $k$, where $k$ represents each integer in the sequence.
4. Step 4: Determine the range of the index. The sequence starts at 4 and ends at 9, so the index $k$ will range from 4 to 9.
5. Step 5: Write the sum in sigma notation. The sum can be expressed as $\sum k_k=4...9$.

Key Concepts

Sigma Notation

Sigma notation is a concise way to represent the sum of a sequence of numbers. It uses the Greek letter sigma (Σ) to indicate summation, followed by an expression that defines the terms to be added. The notation typically includes an index of summation, which specifies the starting and ending values for the variable that represents the terms in the sum.

Index of Summation

The index of summation is a variable used in sigma notation to denote the position of each term in the sequence being summed. It usually starts at a specified lower limit and increments by one until it reaches an upper limit. For example, in the sum Σ from i=1 to n, 'i' is the index that takes on integer values from 1 to n, allowing for the systematic addition of terms.

Arithmetic Sequence

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant. In the case of the sum 4 + 5 + 6 + 7 + 8 + 9, the common difference is 1. Recognizing that the terms form an arithmetic sequence helps in expressing the sum using sigma notation, as it allows for a general formula to represent the terms based on their position in the sequence.