Find 1 + 1/2 + 1/6 + 1/12 + 1/36+...., where we alternately multiply by 1/2 and 1/3 to get the next term.
Separate this into two geometric sequences.
(1 + 1/6 + 1/36 + ...) + (1/2 + 1/12 + ...)
= 1/(1 - 1/6) + (1/2)/(1 - 1/6)
= 6/5 + (1/2)*(6/5)
= 9/5