A group of 5 children and 5 adults are going to the zoo. Child tickets cost $6, and adult tickets cost $8. How much will the zoo
2 answers:
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You can first condense the series to make it simpler to study. If <em>n</em> is odd, then <em>n</em> = 2<em>k</em> - 1, and if <em>n</em> is even, then <em>n</em> = 2<em>k</em> for some <em>k</em> ≥ 1. So for each <em>k</em>, you can pair up the <em>k</em>-th terms of the odd- and even-indexed series.
odd:
even:
So the series can be re-indexed as
By the root test, the series converges, since