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?