Convergence & divergence of geometric series

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Intros
Lessons
  1. Geometric Series Overview:
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Examples
Lessons
  1. Convergence of Geometric Series
    Show that the following series are convergent and find its sum:
    1. n=013n\sum_{n=0}^{\infty} \frac{1}{3^n}
    2. n=1[(58)n1+(1+3n7n)] \sum_{n=1}^{\infty} [(-\frac{5}{8})^{n-1}+(\frac{1+3^n}{7^n})]
    3. n=04n+2234n\sum_{n=0}^{\infty}4^{n+2}2^{3-4n}
    4. n=042(n+2)53n1\sum_{n=0}^{\infty} \frac{4^{2(n+2)}}{5^{3n-1}}
  2. Divergence of Geometric Series
    Show that the following series are divergent:
    1. n=03n12n \sum_{n=0}^{\infty} \frac{3^{n-1}}{2^n}
    2. n=03n+223n\sum_{n=0}^{\infty}3^{n+2}2^{3-n}
    3. n=0[(14)n+(32)n2n]\sum_{n=0}^{\infty}[(\frac{1}{4})^n+(\frac{3}{2})^n2^n]