1520 11 2 2 Infite Series Convergence Definition Source1

1520 11.2 #2 Infinite Series Convergence Definition
https://youtu.be/ndiE_PnfgMQ
In the previous example,

we talked about two different sequences
that occur inside an infinite series.

There's the sequence of individual terms.

Those are the pieces that
are being added together.

And then there's also the
sequence of partial sums,

where S-n means
the sum of the first n terms.

S-4 would be the sum of
the first four terms and so on.

The idea is, if we look at the sequence
of partial sums or the running total,

we can say, if the limit of that
sequence (as n goes to infinity)

is equal to some number,
which we call S, then the series

sum as n goes from one to infinity of ‘a’-n,
we say the series converges.

We actually say that the value
of that sum is this value right here.

We say that the series converges to S.

If the limit does not exist—

So if limit as n goes to infinity
of S-n does not exist,

we say the series converges--
[corrects self] Sorry, diverges.