Sums of Sequences
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Lesson Summary:
In this lesson, you'll learn how to find the sum of arithmetic progressions using a famous result. By rearranging the order of the elements in the addition, we can write a general formula for the sum of an arithmetic progression. The formula is s sub n equals a sub 1 plus a sub n times n or two. By applying this formula, you can solve problems involving sequences that start on an arbitrary number and increase by a constant natural number.
Lesson Description:
Learn how to find the sums of several arithmetic progressions using a famous result.
Questions answered by this video:
- What is the sum of natural numbers from 1 to n?
- How do you find the sum of a sequence?
- What is an arithmetic progression?
- How do you find the sum of an arithmetic progression?
- How do you find the sum of 2 + 4 + 6 + ... + 200?
- How do you find the sum of 1 - 2 + 3 - 4 + ... - 100 + 101?
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Staff Review
This video picks up from the Triangular Numbers video, and it generalizes the sum of natural numbers from 1 to n and gives the formula. This problem is then further generalized to a sequence starting at a1, with each following number increased by a constant d. The discussion gets somewhat involved, but this is a great exercise in mathematical thinking for a higher-level math student.
