How do you find the limit of #sqrt(n^2+n) - (n)# as n approaches #oo#?

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Answer 1 · 2016-04-25T09:49:47

#lim_(n->oo)sqrt(n^2+n)-n =1/2#

#lim_(n->oo)sqrt(n^2+n)-n = lim_(n->oo)((sqrt(n^2+n)-n)(sqrt(n^2+n)+n))/(sqrt(n^2+n)+n)#

#=lim_(n->oo)n/(sqrt(n^2+n)+n)#

#=lim_(n->oo)(n/n)/((sqrt(n^2+n)+n)/n)#

#=lim_(n->oo)1/(sqrt((n^2+n)/n^2)+1)#

#=lim_(n->oo)1/(sqrt(1+1/n)+1)#

#=1/(sqrt(1+0)+1)#

#=1/2#