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Series Partial Sum Sequence

In order to give a meaning to the sum of an infinite series

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

Let

If

for

**Σu**_{n}, we form a sequence of partial sums.Let be any given series, where the terms may be positive or negative.

Let

**S**_{n}= u_{1}+ u_{2}+ …. + u_{n}, be the sum of first n terms of the series**Σu**_{n}. Then**S**_{n}is called the partial sum of the first**n**terms of the given series and the sequence**<S**, where_{n}>**S**, is called the sequence of the partial sums of given series ._{n}= u_{1}+ u_{2}+ …. + u_{n}, ∀ n ϵ NIf

**S**_{n}is known, we can find**u**_{n}and hence the series,for

**u**_{n}= S_{n}– S_{n-1}**∴**From the above discussion, we conclude that a sequence**<S**of partial sums is associated to each series and vice versa._{n}>**∴**We can assign the same behaviour to the series as is exhibited by its sequence <Sn> of partial sums as .**Services: -**Series Partial Sum Sequence Homework | Series Partial Sum Sequence Homework Help | Series Partial Sum Sequence Homework Help Services | Live Series Partial Sum Sequence Homework Help | Series Partial Sum Sequence Homework Tutors | Online Series Partial Sum Sequence Homework Help | Series Partial Sum Sequence Tutors | Online Series Partial Sum Sequence Tutors | Series Partial Sum Sequence Homework Services | Series Partial Sum SequenceSubmit Your Query ???

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