If a1, a2, a3,...., an are n distinct odd numbers not divisible by any prime greater than 5, then (1/a1) +(1/a2) +.....+(1/an)

Question

If a1, a2, a3,...., an are n distinct odd numbers not divisible by any prime greater than 5, then (1/a1) +(1/a2) +.....+(1/an)  (A) < 1 (B) = 1 (C) = 2 (D) < 2

Tardigrade Admin · Accepted Answer

We observe that all the terms of (1/a1) +(1/a2) +.....+(1/an) are contained in (1+(1/3)+(1/32)+.....)(1+(1/5)+(1/52)+.....). ⇒ (1/a1)+(1/a2)+.....+(1/an) < ((1/1-(1)3))((1/1-(1)5)) = (3/2)⋅(5/4) <2

Q. If $a_{1}, a_{2}, a_{3}, ...., a_{n}$ are $n$ distinct odd numbers not divisible by any prime greater than $5$ , then $\frac{1}{a _{1}} + \frac{1}{a _{2}} + ..... + \frac{1}{a _{n}}$

$< 1$

$= 1$

$= 2$

$< 2$

Q. If a1​,a2​,a3​,....,an​ are n distinct odd numbers not divisible by any prime greater than 5, then a1​1​+a2​1​+.....+an​1​

<1

=1

=2

<2

We observe that all the terms of a1​1​+a2​1​+.....+an​1​ are contained in (1+31​+321​+.....)(1+51​+521​+.....). ⇒a1​1​+a2​1​+.....+an​1​<(1−31​1​)(1−51​1​) =23​⋅45​<2

Q. If $a_{1}, a_{2}, a_{3}, ...., a_{n}$ are $n$ distinct odd numbers not divisible by any prime greater than $5$ , then $\frac{1}{a _{1}} + \frac{1}{a _{2}} + ..... + \frac{1}{a _{n}}$

$< 1$

$= 1$

$= 2$

$< 2$