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## Homework Statement

Does the sum of the reciprocals of natural numbers starting with nine converge?

In other words, does Sigma 1/n with n being numbers starting with nine, converge?

## Homework Equations

## The Attempt at a Solution

I know that subsets of the natural numbers with positive density, their sums of reciprocals will diverge. I know that numbers beginning with nine have zero density. So my gut instinct is that is does converge.