Let M be the subset of the Natural numbers consisting of those integers n such that no digit of n in its decimal expression is 5. Prove that
∑n∈M 1/n converges.

Question

Let M be the subset of the Natural numbers consisting of those integers n such that no digit of n in its decimal expression is 5. Prove that 
∑n∈M 1/n converges.

anonymous · Answer

it's divergent n power is smaller than 1

anonymous · Answer

from the comparison test....

anonymous · Answer

I know that $$\sum_{1}^{\infty} 1/n =\infty $$ but for some reason with the subset it converges, and I dont know why

anonymous · Answer

wow this is pretty interesting a proof using 9 instead of 5 can be found here http://www.cut-the-knot.org/arithmetic/algebra/HarmonicSeries.shtml

anonymous · Answer

i can't imagine this proof is trivial, as it is contained in hardy and wright

anonymous · Answer

Hum I will check it out thanks!