Question

Each infinite series has two related sequences: The sequecne of terms and the sequence of partial sums. Discuss what these two sequences and how they differ?

Answer 1

Suppose you have the series 1 + 1/2 + 1/4 + 1/8 + ...

The first sequence is simply the LIST of terms: 1, 1/2, 1/4, etc.

The second sequence is the list of partial sums. These are sums of the first n terms:
sum 1: 1
sum 2: 1 + 1/2 = 3/2
sum 3: 1 + 1/2 + 1/4 = 7/4
etc.

You should be able to take it from here.