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Numerade Educator

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Problem 54 Medium Difficulty

Determine whether the sequence converges or diverges. If it converges, find the limit.
$ \left \{ \frac {1}{1}, \frac {1}{3}, \frac {1}{2}, \frac {1}{4}, \frac {1}{3}, \frac {1}{5}, \frac {1}{4}, \frac {1}{6}, . . . \right \} $

Answer

converges to 0

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Video Transcript

this problem, One of the hardest parts might just be figuring out exactly what the pattern is here. So for odd in are they in terms? Car one over one. Went over to one over three, one over four. And I'm sure you can see the pattern f and for even in Are they in terms? R one over three, one over four, one over five, one over six. And I'm sure you can see the pattern there as well. Okay, Both of these sequences converge to zero. Right. This sequence clearly goes to zero. This sequence clearly goes to zero. Therefore, the sequence sequence made up of just the's A in terms converges to zero. Right, because this is just a combination of both of these sequences here. So both those sequences converged to zero. Then the larger sequence must also converged to zero