Friday, 11 September 2015

real analysis - Limit of nsqrtn2+2n

bn=nn2+2n. Taking (1n)0 as given, using Algebraic Limit Theorem, show lim(bn) exists and find value



The question also says to use the fact that if (xn)x then xnx. I've simplified the bn down to n(11+2n), which appears to be going to zero as n gets large using the algebraic limit theorem. However, I know that limbn=1. I'm stuck on how to prove this, and I haven't found any help elsewhere. Any advice would be helpful!

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