First slide

Introduction to P.M.I

Question

For a positive integer n, Let $a (n) = 1 + \frac{1}{2} + \frac{1}{3} + \frac{1}{4} + \dots + \frac{1}{2^{n} - 1}$ .then

Moderate

A

$a (100) \leq 100$
B

$a (100) > 100$
C

$a (200) \leq 100$
D

$a (200) > 100$

Solution

It can be proved by induction that $\frac{n}{2} > a (n) \leq n$ .
$∴ \frac{200}{2} < a (200) \Rightarrow a (200) > 100 and a (100) \leq 100$ .

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