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Home » Math Homework Help » Algebra Homework Help » Sum of a Series
Sum of a Series
If a sequence <Sn>, of the partial sums of a series Σun converges to a finite quantity ‘s’, then ‘s’ is called the sum of the given series Σun 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.

Theorem 1:
The replacement, addition or omission of a finite number of terms of a series Σun 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 series



which is a finite quantity and, therefore, the sequence <Sn> of the partial sums converges to 2 and consequently Σun is convergent.

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