Use of Sigma Notation (Geometric)
Key points
- Just like arithmetic series, geometric series can be abbreviated in summation, or sigma notation.
- The elements of sigma notation are the upper and lower limits, and a formula for the terms.
Sigma Notation is the shorthand way to write the sum of a finite geometric series.
- It is based on the Greek letter sigma.
- The lower limit, at the bottom of the expression, is the number of term you are starting at.
- The upper limit, at the top of the expression, is the number of the last term of the finite arithmetic series.
- The expression on the right hand side of sigma notation is the formula for the value of a term based on the term number.
Expressing a finite geometric series in sigma notation requires derivation of the different elements, as seen to the left.
- Find the common ratio by dividing two consecutive values.
- Substitute this common ratio and the value of the first term back into the equation, then derive an expression for the value of the term based on the number of the term.
- Use this derived expression to find the upper limit.
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