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### Course: Calculus 2>Unit 1

Lesson 3: Summation notation review

# Worked examples: Summation notation

Summation notation uses the sigma Σ symbol to represent sums with multiple terms. See some more involved examples of how we read expressions in summation notation.

## Want to join the conversation?

• Say you were given a series like:

4/3, -1, 3/4...

How would you find the formula for the terms? (like in the first example of the video?)
• The equation for this would be that of a geometric sequence and the equation would be (4/3)*(-3/4)^(x-1). The way you would put it is have three at the top of the `sigma` set i equal to 1, and have the equation as (4/3)*(-3/4)^(x-1).
• For the first example, isn't option B only a sum up to the first 3 terms?
• No, because we start with n=0, so we get 4 terms:
n=0, n=1, n=2, n=3
• If you were given something like [62, 73, 84, 95], how would you find the summation notation for this?
• If the difference is constant, as it is here, you can do something like making the expression the first term + index * the difference and make the boundaries 0 and the last term - 1. In your example, it would be
3
Σ (62+11i)
i=0
• Would we deal with Figuring out the pattern without choices ?
• What is the summation notation for 1/2 + 2/2 + 3/2 + 4/2 + 5/2?
• If we factor out 1∕2, we get
1∕2 ∙ (1 + 2 + 3 + 4 + 5) = 1∕2 ∙ ∑𝑘, as 𝑘 goes from 1 to 5.
• What is the summation notation for 1/2 + 4/5 + 9/10 + 16/17?
• Observe that the numerators form the first four positive perfect squares (in order), and the denominators are 1 more than the corresponding numerators. So the nth term of the series is (n^2)/(n^2+1), for 1<=n<=4.

So the sum of this four-term series can be written as

sum n from 1 to 4 of (n^2)/(n^2+1).
• so how do you actually do the math, say if the n was 1 to 500 in the situation above?
• So the content you are looking is arithmetic sequence. Just type that into the search bar. There is also geometric sequence.
• What if

(1-2+3-4+5-6+7-8+9-10)

how can we find the summation notation for this? thanks