Show That a Sequence Converges
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Define . Show that the sequence converges.
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A sequence is shown to converge. The solution is detailed and well presented.
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Question:
Define . Show that the sequence converges.
Answer:
First of all it's sensible to get a feel for what the terms actually look like:
a1 = 1
a2 = 7/5 = 1.4
a3 = 41/29 = 1.41379...
a4 = 239/169 = 1.41420...
It certainly appears that the terms are increasing and that they converge to 1.414...
To find the actual limit we solve
rearranging we get so
So the limit is the ...
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