Suppose a1, a2,…, an are n distinct odd natural numbers not divisible by any prime greater than 5, then value of the expression 1a1+1a2+…1ancannot exceed

# Suppose , an are n distinct odd natural numbers not divisible by any prime greater than 5, then value of the expression $\frac{1}{{a}_{1}}+\frac{1}{{a}_{2}}+\dots \frac{1}{{a}_{n}}$cannot exceed

1. A

2

2. B

1

3. C

$\frac{1}{2}$

4. D

none of these

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### Solution:

Note that

$\begin{array}{l}\frac{1}{{a}_{1}}+\frac{1}{{a}_{2}}+\dots +\frac{1}{{a}_{n}}\\ <\left(1+\frac{1}{3}+\frac{1}{{3}^{2}}+\dots \right)\left(1+\frac{1}{5}+\frac{1}{{5}^{2}}+\dots \right)\\ =\left(\frac{1}{1-1/3}\right)\left(\frac{1}{1-1/5}\right)=\frac{15}{8}<2\end{array}$

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