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Sum of a Series

If a sequence

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

which is a finite quantity and, therefore, the sequence

**<S**, of the partial sums of a series_{n}>**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 or simply as**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.

**The replacement, addition or omission of a finite number of terms of a series**

Theorem 1:Theorem 1:

**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**.**Example:**Show that the serieswhich is a finite quantity and, therefore, the sequence

**<S**of the partial sums converges to_{n}>**2**and consequently**Σu**_{n}is convergent.**Services: -**Sum of a Series Homework | Sum of a Series Homework Help | Sum of a Series Homework Help Services | Live Sum of a Series Homework Help | Sum of a Series Homework Tutors | Online Sum of a Series Homework Help | Sum of a Series Tutors | Online Sum of a Series Tutors | Sum of a Series Homework Services | Sum of a SeriesSubmit Your Query ???

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