Guided Example #1 - Sequences and Series
Determine whether the series ∞∑n=15 (12)n is convergent or divergent. If it is convergent, find its sum.
Let's start by writing down some of the first terms in the series.
∞∑n=15 (12)n=5 (12)+5 (12)2+5 (12)3+5 (12)4+⋯
Note that this is a geometric series of the form ∞∑n=1arn with |r|=12<1 and, hence, it converges to a1-r=51-12=10.
Let's start by writing down some of the first terms in the series.
∞∑n=15 (12)n=5 (12)+5 (12)2+5 (12)3+5 (12)4+⋯
Note that this is a geometric series of the form ∞∑n=1arn with |r|=12<1 and, hence, it converges to a1-r=51-12=10.