The harmonic series:

is divergent, i.e. sums to

.

This geometric series:

is convergent to 2.

In general, is there a way to know if removing all the elements of a convergent series, from a divergent series, if the result will be divergent or convergent?

It makes sense to me, that if I were to remove

from the harmonic series, it would remain divergent.

is still

after all. But how much can I take away from something infinite, and have it remain so? Thinking the other way, how much do I have to remove to get it to converge?

-Scott

P.S.

Is Calculus the right forum for questions on series and sequences?