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Mathematics - Sequence & Series Question with Solution | TestHub

MathematicsSequence & SeriesSpecial sequences/seriesMedium2 minQB

MathematicsMediumsingle choice

Let $d_{1}, \dots, d_{k}$ be all positive divisors of a positive integer $n$ , including $1, n$ . If their sum is 72 , find $\sum_{i = 1}^{k} 1/ d_{i}$ .

Options:

Answer:

Solution:

The map $d \mapsto n / d$ permutes the divisors. Thus $\sum 1/ d = \sum (n / d) / n = (\sum d) / n = 72/ n$ .

Stream:JEESubject:MathematicsTopic:Sequence & SeriesSubtopic:Special sequences/series

⏱ 2mℹ️ Source: QB

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