Math Problem Statement

Use the properties of summation and the Summation Formulas Theorem to evaluate the sum: Σ (from i = 1 to 10) of 8.

Solution

The summation shown in the image is:

i=1108\sum_{i=1}^{10} 8

This represents a constant sum, where the value "8" is added for each value of ii from 1 to 10. Since 8 is a constant, you can simply multiply 8 by the number of terms in the summation.

The number of terms is from i=1i = 1 to i=10i = 10, so there are 10 terms.

Thus, the sum is:

i=1108=8×10=80\sum_{i=1}^{10} 8 = 8 \times 10 = 80

Would you like any further details, or do you have any other questions?

Here are 5 related questions to expand on this:

  1. What is a general formula for the sum of a constant over nn terms?
  2. How does the summation change if the constant is not 8 but any other number?
  3. Can you explain the difference between summing a constant and summing a variable term?
  4. How does this concept apply when summing arithmetic series or geometric series?
  5. What would happen if the lower limit of summation changed from 1 to another number, like 5?

Tip: When dealing with constant summations, the sum is always the product of the constant and the number of terms in the summation.

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Math Problem Analysis

Mathematical Concepts

Summation
Algebra

Formulas

Summation of constants: Σ c = c * n

Theorems

Summation Formula Theorem

Suitable Grade Level

Grades 7-9