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Home » Math Homework Help » Algebra Homework Help » Series Partial Sum Sequence
Series Partial Sum Sequence
In order to give a meaning to the sum of an infinite series Σun, we form a sequence of partial sums.

Let be any given series, where the terms may be positive or negative.

Let Sn = u1 + u2 + …. + un, be the sum of first n terms of the series Σun. Then Sn is called the partial sum of the first n terms of the given series and the sequence <Sn>, where Sn = u1 + u2 + …. + un, ∀ n ϵ N, is called the sequence of the partial sums of given series   .

If Sn is known, we can find un and hence the series,

for un = Sn – Sn-1

From the above discussion, we conclude that a sequence <Sn> of partial sums is associated to each series   and vice versa.

We can assign the same behaviour to the series   as is exhibited by its sequence <Sn> of partial sums as .

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