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education/math/MATH1220 (calc II)/Sequences and Series.md

@@ -147,4 +147,9 @@ The behavior a given power series falls into one of three cases:
 		$$ \frac{x}{3}$$
 2. For a geometric series, it converges when the ratio $r$ is less than one. Written as an equality, this gives us:
 $$ |r| < 1 \to |\frac{x}{3}| < 1 \to |x| < 3 $$
-This means that the interval of convergence is $(-3, 3)$, given it diverges at both interval endpoints.
+This means that the interval of convergence is $(-3, 3)$, given it diverges at both interval endpoints.
+
+## Integral test for series
+The integral test determines if an infinite series converges or diverges by comparing it to an improper integral. If the integral diverges ($= \infty$), then the series also diverges. If the integral converges, then the series is 
+
+Given the series $\sum_{n=0}^\infty a_n$, the improper integral would be of the below form: