It is given in the question that d|k means d is a positive of k. But, what does that mean? Please just give an answer for this because rest I have to try it out myself.
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2It's missing a word. Positive "divisor" of $k$. It means $k$ is divisible by $d$, and $d$ is positive. – Zavosh Aug 26 '13 at 01:36
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For example, the sum of the positive divisors of $12$ is $1+2+3+4+6+12$. – André Nicolas Aug 26 '13 at 01:45
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m<n but the sum of positive divisors of m and n are equal. This implies that m has larger divisors(in terms of value). The values of d for m would be greater than that for n. Thus, 1/d for m would be less than that for n. Thus I choose option (A). Is my thinking correct? – Rajath Radhakrishnan Aug 26 '13 at 01:52
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Your answer is not correct. For each divisor $d$ of $m$, $\frac md$ is also a divisor, so $$\sum_{d|m}\frac md=m\sum_{d|m}\frac 1d=\sum_{d|m}d\\\sum_{d|m}\frac 1d=\frac 1m\sum_{d|m}d\\\sum_{d|n}\frac 1d=\frac 1n\sum_{d|n}d\lt \frac 1m\sum_{m|d}d=\sum_{d|m}\frac 1d$$
Ross Millikan
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