Publish On: 2019-05-25

# jollay

Total Post: 559

## Question: Describe the sum of a series

Reply On: 2013-10-08

# Mjay Jollay

Total Post: 0

## ANS: Describe the sum of a series

If a sequence <S

The following theorems are the general convention for converges or divergence of a series.

_{n}>, of the partial sums of a series Σu_{n}converges to a finite quantity ‘s’, then ‘s’ is called the sum of the given series Σu_{n}and is generally written as s = = u_{1}+ u_{2}+ …. + u_{n}+ …. or simply as .**Remark 1:****the series Σu**_{n}diverges to +∞ (plus infinity) or to -∞ (minus infinity).**Remark 2:**We know that the convergence of a sequence always depends upon from and after some fixed terms, therefore, the nature of the series remains unaltered if a finite number of terms are taken out from the series.The following theorems are the general convention for converges or divergence of a series.

**Theorem 1:**The replacement, addition or omission of a finite number of terms of a series Σu_{n}has no effect on its convergence.**Theorem 2:**The convergence of a series remains unchanged if each of its terms is multiplied by a constant by a constant k, k ≠ 0.Like Us On Facebook for All Latest Updates