It's an alternating series that is not absolutely convergent.

determining if it is convergent or divergent + taylor series

Finally, the convergent series defines a holomorphic function ƒ(z) on the open annulus.

Finally, the convergent series defines a holomorphic function f(z) on the open annulus.

For example, the Orlicz-Pettis theorem says that in Banach spaces the classes of weakly subseries convergent and norm unconditionally convergent series coincide.

Verify that a linear combination of convergent series is convergent.

Cauchy claimed that a convergent series of continuous functions has a continuous limit.

Cauchy had proved that a convergent series of terms, each of which is continuous, converges to a continuous function.

∑ a n {\displaystyle \sum a_{n}} is a convergent series,

∑ a n {\displaystyle \sum a_{n}} is a convergent series,

Cauchy in 1821 published a faulty proof of the false statement that the pointwise limit of a sequence of continuous functions is always continuous.

I calculated the distance covered for each journey, I found the general term of a convergent series that I added up and I found 100".

In 1936, Rademacher gave a formula for p(n) as a convergent series.