The harmonic series notably does not have this property, although if one removes all the numbers which have the digit nine somewhere in the denominator, the resulting series does.
Dini's theorem says that if something has a weak form of this property and ful- lls other conditions, then it also has a stronger form of this property. Bertrand ￼ ￼ ￼ ￼ ￼ ￼ ￼ ￼ ￼ and Dirichlet both name conditions to determine whether something has this property. Hadamard's theorem gives a means for determining this quantity's namesake radius. If a series has the conditional variety of this property, then its sum can be changed by rearranging its values. The harmonic series notably does not have this property, although if one removes all the numbers which have the digit nine somewhere in the denominator, the resulting series does. For ten points, identify this property held by a series or sequence whose limit at in nity exists. 
Dini's theorem says that if something has a weak form of this property and ful- lls other conditions, then it also has a stronger form of this property.
convergence [accept word forms] 