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" (v) "lim(n rarr oo)[(1)/(n)+(sqrt(n^(2...

" (v) "lim_(n rarr oo)[(1)/(n)+(sqrt(n^(2)-1^(2)))/(n^(2))+(sqrt(n^(2)-2^(2)))/(n^(2))+......---cdots+cdots+(sqrt(n^(2)-(n-1)^(2)))/(n^(2))]

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lim_(nrarroo) [(1)/(n)+(sqrt(n^(2)-1^(2)))/(n^(2))+(sqrt(n^(2)-2^(2)))/(n^(2))+...+(sqrt(n^(2)-(n-1)^(2)))/(n^(2))]

lim_(n rarr oo) n(sqrt(n^(2)+8)-n) =

lim_(n rarr oo) n(sqrt(n^(2)+6)-n) =

lim_(n rarr oo)(sqrt(n^(2)+n)-sqrt(n^2+1))

lim_(n rarr oo) sum_(r=0)^(n-1) 1/(sqrt(n^(2)-r^(2))) =

lim_(n to oo)[(1)/(sqrt(n^(2)-1^(2)))+(1)/(sqrt(n^(2)-2^(2)))+(1)/(sqrt(n^(2)-3^(2)))+...+(1)/(sqrt(n^(2)-(n-1)^(2)))]

Lt_(n rarr oo)[(1)/(n)+(1)/(sqrt(n^(2) -1^(2)))+(1)/(sqrt(n^(2)-2^(2)))+... "to n terms"]

{:(" "Lt),(n rarr oo):} [(sqrt(n^(2)-1^(2)))/(n^(2))+(sqrt(n^(2)-2^(2)))/(n^(2))+(sqrt(n^(2)-3^(2)))/(n^(2)).+....n "terms"]=

lim_(nrarroo)((1)/(sqrt(n^(2)))+(1)/(sqrt(n^(2)-1^(2)))+(1)/(sqrt(n^(2)-2^(2)))+....+(1)/(sqrt(n^(2)-(n-1)^(2)))) is equal to

underset(nrarroo)lim[(1)/(sqrt(n^(2)-1^(2)))+(1)/(sqrt(n^(2)-2^(2)))+(1)/(sqrt(n^(2)-3^(2)))+...+(1)/(sqrt(n^(2)-(n-1)^(2)))]