This is related to the the May 16 post, but takes only the prime indexed terms. Does it still diverge?
Hint
Transform the product into a sum
Hint
The harmonic series 1 + 1/2 + 1/3 + … 1/n +… diverges
This is related to the the May 16 post, but takes only the prime indexed terms. Does it still diverge?
Transform the product into a sum
The harmonic series 1 + 1/2 + 1/3 + … 1/n +… diverges
I don’t know how to begin proving it, but the more I run this series out, bigger it gets. The conditions of the equation are such that it will always have a consistently non-zero rate of increase, even though that rate of increase decreases each time the formula is cycled ((pn/pn-1) will always be more than (pn+1/pn+1-1), nonetheless any and every (pn/pn-1) will be >1). The divergence will be glacial, but definite.
I can confirm that your intuition for divergence is correct.