Find each indicated sum. ${\sum }_{i=5}^{9}11$

Verified step by step guidance

1. Identify the summation notation given: \(\sum_{i=5}^{9} 11\). This means you need to add the constant value 11 for each integer value of \(i\) starting from 5 up to 9.
2. Determine how many terms are in the sum. Since \(i\) goes from 5 to 9, count the integers: 5, 6, 7, 8, 9. There are 5 terms in total.
3. Since the term being summed is a constant (11), the sum can be calculated by multiplying the constant by the number of terms. So, the sum is \$11 \times 5$.
4. Write the expression for the sum explicitly: \(\sum_{i=5}^{9} 11 = 11 + 11 + 11 + 11 + 11 = 11 \times 5\).
5. To find the final sum, multiply 11 by 5. This will give you the total sum of the series.

Key Concepts

Summation Notation (Sigma Notation)

Summation notation uses the Greek letter sigma (Σ) to represent the sum of a sequence of terms. The expression specifies the index of summation, its starting and ending values, and the general term to be added. Understanding this notation is essential to correctly interpret and evaluate sums.

Evaluating Constant Sums

When the term inside the summation is a constant, the sum equals the constant multiplied by the number of terms. For example, summing a constant 'c' from i = m to n results in c × (n - m + 1). This simplifies calculations without adding the constant repeatedly.

Index of Summation and Limits

The index of summation (usually i) runs from the lower limit to the upper limit, inclusive. Correctly identifying these limits is crucial to determine how many terms are summed and to avoid errors in the total sum calculation.