The series $\sum _ { n = 1 } ^ { \infty } \frac { ( - 1 ) ^ { n } } { ( 6 n + 3 ) ! }$ converges

Name: The series $\sum _ { n = 1 } ^ { \infty } \frac { ( - 1 ) ^ { n } } { ( 6 n + 3 ) ! }$ converges
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Quizplus · Accepted Answer

The series is alternating and its terms decrease in absolute value. Also, the denominator grows very fast, so by the alternating series test, the series converges.

The Series ∑n=1∞(−1)n(6n+3)!\sum _ { n = 1 } ^ { \infty } \frac { ( - 1 ) ^ { n } } { ( 6 n + 3 ) ! }∑n=1∞​(6n+3)!(−1)n​

The Series $\sum _ { n = 1 } ^ { \infty } \frac { ( - 1 ) ^ { n } } { ( 6 n + 3 ) ! }$