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education/math/MATH1220 (calc II)/Sequences.md
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@@ -85,4 +85,6 @@ $$ = \sum_{n=1}^\infty \frac{35}{7}(\frac{1}{7})^{n-1}* 2^{n-1} = \sum_{n = 1}^\
$$\sum_{n=1}^{\infty}35(7^{-n} * 2^{n-1}) = \dfrac{\frac{35}{7}}{1-\frac{2}{7}}$$ $$\sum_{n=1}^{\infty}35(7^{-n} * 2^{n-1}) = \dfrac{\frac{35}{7}}{1-\frac{2}{7}}$$
# Divergence Test # Divergence Test
If $\lim_{n \to \infty} a_n \ne 0$ then $\sum_{a} **If $\lim_{n \to \infty} a_n \ne 0$ then $\sum_{n=1}^\infty a_n$diverges.**
The divergence test only tells us that if the limit does not equal zero, then the series diverges. If the limit is zero, it doesn't necessarily mean the series converges.