Consider the sequence of real number { } defined recursively by Show that the sequence is convergent and find its limit.
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Originally Posted by thaopanda Consider the sequence of real number { } defined recursively by Show that the sequence is convergent and find its limit. 1.- prove inductively that the sequence is bounded above , by 3 say. 2.- prove inductively that a_n <= a_(n+1) (monot. ascending) 3.- thus the limit exists by a theorem. Now use a_(n+1) = sqrt(6 + a_n) and arithmetic of limits to find the limit. Tonio
wow, I was actually really close to that. I started to use induction, but then I thought I had to prove it was cauchy or something since that's all my professor forces into our head.... thanks!
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