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Summation notation

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Calculus II

Definition

Summation notation, often represented by the Greek letter sigma ($\Sigma$), is a concise way to express the sum of a sequence of numbers. It is commonly used to approximate areas under curves and in various mathematical analyses.

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5 Must Know Facts For Your Next Test

  1. Summation notation uses an index variable (usually $i$, $j$, or $k$) that runs from a lower bound to an upper bound.
  2. The general form is $\sum_{i=a}^{b} f(i)$, where $a$ is the lower limit, $b$ is the upper limit, and $f(i)$ is the function being summed.
  3. In calculus, summation notation can be used to represent Riemann sums which approximate integrals.
  4. Summation properties include linearity: $\sum_{i=1}^{n} (a_i + b_i) = \sum_{i=1}^{n} a_i + \sum_{i=1}^{n} b_i$ and constant multiplication: $\sum_{i=1}^{n} c \cdot a_i = c \cdot \sum_{i=1}^{n} a_i$.
  5. It is important for understanding definite integrals in Calculus II as they are the limits of Riemann sums.

Review Questions

  • What does the index variable in summation notation represent?
  • How would you write the sum of squares from 1 to n using summation notation?
  • What are two key properties of summation notation that simplify calculations?
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