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Course: AP®︎ Calculus AB > Unit 6
Lesson 3: Риманы нийлбэр, нийлбэрийн тэмдэглэгээ, тодорхой интеграл тэмдэглэгээ- Summation notation
- Worked examples: Summation notation
- Summation notation
- Riemann sums in summation notation
- Riemann sums in summation notation
- Worked example: Riemann sums in summation notation
- Riemann sums in summation notation
- Definite integral as the limit of a Riemann sum
- Definite integral as the limit of a Riemann sum
- Worked example: Rewriting definite integral as limit of Riemann sum
- Worked example: Rewriting limit of Riemann sum as definite integral
- Definite integral as the limit of a Riemann sum
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Summation notation
We can describe sums with multiple terms using the sigma operator, Σ. Learn how to evaluate sums written this way.
Summation notation (or sigma notation) allows us to write a long sum in a single expression.
Unpacking the meaning of summation notation
This is the sigma symbol: . It tells us that we are summing something.
Let's start with a basic example:
This is a summation of the expression for integer values of from to :
Notice how we substituted , , and into and summed the resulting terms.
We can start and end the summation at any value of . For example, this sum takes integer values of from to :
We can use any letter we want for our index. For example, this expression has for its index:
Some summation expressions have variables other than the index. Consider this sum:
Notice that our index is , not . This means we substitute the values into , and remains unknown:
Key takeaway: Before evaluating a sum in summation notation, always make sure you identified the index, and that you are only substituting into that index. Other unknowns should remain as they are.
Want more practice? Try this exercise.
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