Sunday, October 9, 2016

real analysis - Calculate limnto+infty(sqrtn2+nn)











Could someone help me through this problem?
Calculate limn+(n2+nn)


Answer



We have:




n2+nn=(n2+nn)(n2+n+n)n2+n+n=nn2+n+n


Therefore:



n2+nn=11+1n+1



And since: limn+1n=0



It follows that:



limn+(n2+nn)=12



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