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Mathematics - Sequence & Series Question with Solution | TestHub

MathematicsSequence & SeriesG.P.Medium2 minQB

MathematicsMediumsingle choice

If $a_{1}, \dots, a_{n}$ are distinct odd natural numbers with no prime divisor greater than 5 , then which listed value is the least strict upper bound for $1/ a_{1} + \dots + 1/ a_{n}$ ?

Options:

Answer:

Solution:

Each number is $3^{r} 5^{s}$ with nonnegative integers $r, s$ . A finite sum of distinct reciprocals is strictly below the full double geometric series $\sum_{r, s \geq 0} 3^{- r} 5^{- s} = (3/2) (5/4) = 15/8$ .

Stream:JEESubject:MathematicsTopic:Sequence & SeriesSubtopic:G.P.

⏱ 2mℹ️ Source: QB

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