smallest positive integer n

\hspace{-16}$Find the smallest positive Integer $\mathbf{n}$ such that \\\\ $\mathbf{\sqrt{n}-\sqrt{n-1}<0.01}$

5 Answers

Is it 2501?

yeah even I think its 2501.

\sqrt{n}-\sqrt{n+1}<.01

\Rightarrow (\sqrt{n})^2<(\sqrt{n+1}+.01)^2

\Rightarrow n<n-1+.02\sqrt{n-1}+.0001

\Rightarrow 1<.02\sqrt{n-1}+.0001

\Rightarrow 50<\sqrt{n-1}+.005

Edit: sorry the ans. is 2501.
Thank you @rishabh

@arnab
what hav you done in the second step?

@arnab.
i think under the root it should have been n-1 rather then n+1 in the 2nd step RHS.

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