### 4 videos in "Summations"

## Sums of Sequences

(
download video
)

Learn how to find the sums of several arithmetic progressions using a famous result.

- 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?

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.