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

A
2
B
1
C
$\frac{1}{2}$
D
none of these

Solution:

Note that

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

Suppose $a 1, a 2, \dots$ , 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

Solution:

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