Chapter 7: Q. 3 (page 614)
What is meant by the sequence of partial sums for a series? Why does it make sense to define the convergence of a series in terms of the convergence of its sequence of partial sums?
Short Answer
The sequence of partial sums of a series is the partial sum of the first through nth terms.
As
That's what, it makes a sense to define the convergence of a series in terms of the convergence of its sequence of partial sums.