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ISI B.Math(Hons.) Admission Test 2009 Problem 3

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April 9, 2012
functiongeometric seriesabsolute valuealgebra unsolvedalgebra

Problem Statement

Let 1,2,3,4,5,6,7,8,9,11,12,⋯1,2,3,4,5,6,7,8,9,11,12,\cdots be the sequence of all positive integers which do not contain the digit zero. Write {an}\{a_n\} for this sequence. By comparing with a geometric series, show that ∑k=1n1ak<90\sum_{k=1}^n \frac{1}{a_k} < 90.
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