List of top Logical Reasoning Questions on Number Systems

The sum of the following infinite series is
$2+ \frac{1}2 + \frac{1}3 + \frac{1}4 + \frac{1}8 + \frac{1}9 + \frac{1}{16} + \frac{1}{27}+ .....$

How many 4-digit positive integers divisible by 3 can be formed using only the digits {1, 3, 4, 6, 7}, such that no digit appears more than once in a number?