Saturday, 13 September 2014

real analysis - Limit exercise from Rudin: limlimitsntoinftysqrtn2+nn




This is Chapter 3, Exercise 2 of Rudin's Principles.



Calculate lim.



Hints will be appreciated.


Answer



Hint:
\frac{\sqrt{n^2+n}-n}{1} = \frac{\sqrt{n^2+n}-\sqrt{n^2}}{1}\times \frac{\sqrt{n^2+n}+\sqrt{n^2}}{\sqrt{n^2+n}+\sqrt{n^2}} = \cdots
I will expand more if needed.



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