Need help with this limit please $\displaystyle \lim{\sqrt{n^2+n}-n}$ n->$\displaystyle \infty$ I know the answer is 1/2
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Originally Posted by dlbsd Need help with this limit please $\displaystyle \lim{\sqrt{n^2+n}-n}$ n->$\displaystyle \infty$ I know the answer is 1/2 On rationalising the numerator $\displaystyle \lim_{n\to \infty}\frac{n}{\sqrt{n^2+n}+n}=\lim_{n\to \infty}\frac{1}{\sqrt{1+\frac{1}{n}}+1}=\frac{1}{1 +1}=\frac{1}{2}$
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