Thread: Math Quiz 7
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Unread 27-03-2015, 22:11
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Re: Math Quiz 7

Quote:
Originally Posted by Caleb Sykes View Post
This statement is false. It has been proven that Sk=1OO (k/(k+3))2k diverges.
Oops, that's what I get for not going back and refreshing my memory.

How about this one:
  • JaredRachel has shown that (k/(k+3))2k (the terms, not the series sum) converges to e-6 ~ .00248 ~ 1/403.
  • This means that for every k sufficiently large, (k/(k+3))2k < 1/4 (actually I believe this is true for all of them)
  • As k/(k+3) is positive, (k/(k+3))k < 1/2 for sufficiently large k.
  • Therefore, for every k sufficiently large, (k/(k+3))k2 < 1/2k
  • We know Sk=1OO 1/2k, converges at 1.0.
  • By the comparison test, Sk=1OO (k/(k+3))k2 converges.
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Last edited by GeeTwo : 27-03-2015 at 22:47.
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