Geometric Series

• The sum of all terms of a geometric sequence
• Series with a constant ratio between successive terms

Formula

Finite Geometric Series

• For $r \neq 1$
• $a + ar + ar^2 + ar^3 + ... + ar^{n - 1} = \displaystyle\sum_{k=0}^{n-1} ar^k = a(\frac{1 - r^n}{1 - r})$
  • $a$ is the first term
  • $r$ is the common ratio
  • $n$ is the term you are looking for

Infinite Geometric Series

• Absolute value for $r$ must be less than $1$ for the series to converge
  • If $r \gt 1$ then the sum is $\infty$
• $a + ar + ar^2 + ar^3 + ... + ar^{n - 1} = \displaystyle\sum_{k=0}^{\infty} ar^k = \frac{a}{1 - r}$

Math Series