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n^0.5-(n-1)^0.5<0.01

Source: 1978 AHSME Problem 18

June 6, 2014
AMC

Problem Statement

What is the smallest positive integer nn such that n−n−1<.01\sqrt{n}-\sqrt{n-1}<.01?
<spanclass=′latex−bold′>(A)</span>2499<spanclass=′latex−bold′>(B)</span>2500<spanclass=′latex−bold′>(C)</span>2501<spanclass=′latex−bold′>(D)</span>10,000<spanclass=′latex−bold′>(E)</span>There is no such integer<span class='latex-bold'>(A) </span>2499\qquad<span class='latex-bold'>(B) </span>2500\qquad<span class='latex-bold'>(C) </span>2501\qquad<span class='latex-bold'>(D) </span>10,000\qquad <span class='latex-bold'>(E) </span>\text{There is no such integer}
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