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education/math/MATH1220 (calc II)/Sequences.md
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@ -69,9 +69,12 @@ $$ \lim_{n \to \infty} \frac{n(n+1)}{2} = \infty $$
Given the above info, the limit is non-zero, so we know that the series diverges. Given the above info, the limit is non-zero, so we know that the series diverges.
## Geometric Series # Geometric Series
A geometric series of the form: A geometric series of the form:
$$ \sum_{n = 1}^\inifty ar^{n-1} = \sum_{n=0}^\infty ar^n $$ $$ \sum_{n = 1}^\infty ar^{n-1} = \sum_{n=0}^\infty ar^n $$
Converges to $\dfrac{a}{1-r}$ if $|r| < 1$ or diverges if $|r| >= 1$. Converges to $\dfrac{a}{1-r}$ if $|r| < 1$ or diverges if $|r| >= 1$.
# E # Examples:
> Determine if the series $\sum_{n=1}^{\infty}35(7^{-n} * 2^{n-1})$ diverges or converges. If it converges, state where.