Summing Specific Reciprocals
Algebra
Level
3
\[1+\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}+\dfrac{1}{6}+\dfrac{1}{8}+\dfrac{1}{9}+\dfrac{1}{12}+\dfrac{1}{16}+\dfrac{1}{18}+\cdots = \, ?\]
Clarification: The denominators are all positive integers whose prime divisors are either 2 and/or 3 only. In other words, they exclude all numbers with a prime factor greater than 3.
by
Julian Yu