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Series Homework Question: Divergent or Convergent? Methods Compared
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[QUOTE="Of Mike and Men, post: 5458938, member: 558306"] [h2]Homework Statement [/h2] I was watching a PatrickJMT video on ratio test and he gave this problem. I solved it before he did, and he got that it was divergent. He didn't simplify it initially, so our methods of approach are different. Did I do something wrong? I checked my calculator to make sure all my simplifications were correct. So I'm assuming I did something near the limit portion that was incorrect (if at all). Thanks ∞ ∑ n/3[SUP]1+3n[/SUP] n=1 [h2]Homework Equations[/h2][h2]The Attempt at a Solution[/h2] ∞ ∑ n/3[SUP]1+3n[/SUP] = n/(3⋅27[SUP]n[/SUP]) n=1 lim |(n+1)/(3⋅27[SUP]n+1[/SUP]) / (n/3 *27[SUP]n[/SUP])| n→∞ = lim |(n+1)/n| * (1/27) n→∞ = 1 * 1/27 =1/27 < 1 Convergent by Ratio Test [/QUOTE]
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Series Homework Question: Divergent or Convergent? Methods Compared
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