Publish On: 2019-05-17

# ally

Total Post: 571

## Question: Explain the sequence of partial sums of an infinite series

Reply On: 2013-10-08

# Mjay Jollay

Total Post: 0

## ANS: Explain the sequence of partial sums of an infinite series

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

Let = u

Let S

If S

for u

∴ From the above discussion, we conclude that a sequence <S

∴ We can assign the same behaviour to the series as is exhibited by its sequence <S

_{n}, we form a sequence of partial sums.Let = u

_{1}+ u_{2}+ u_{3}+ …. + u_{n}+ …. be any given series, where the terms may be positive ir 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_{n}>, where S_{n}= u_{1}+ u_{2}+ …. + u_{n}, ∀ n ϵ N, is called the sequence of the partial sums of given series .If 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

_{n}> 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 <S

_{n}> of partial sums as n∞.Like Us On Facebook for All Latest Updates