Find the sum of the first 100 terms for the sequence sigma_{n = 1}^{infinity} 2 / n^2 + 4n + 3...


Find the sum of the first 100 terms for the sequence

{eq}\displaystyle \sum_{n = 1}^{\infty}\ \dfrac {2}{n^2 + 4n + 3} {/eq} and then find the sum {eq}s {/eq}.

Sum of Series:

The series sum is evaluated by finding the limit of a given series. For the geometric type series, the sum is evaluated by a formula where first term is divided by one minus the common ratio. If it is not then using the well-known series expansion can help or using the technique of brute force.

Answer and Explanation: 1

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  • The series {eq}\sum\limits_{n = 1}^\infty {\dfrac{2}{{{n^2} + 4n + 3}}} \tag{1} {/eq}

The sum of the series (1) upto 100 terms is given...

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Infinite Series & Partial Sums: Explanation, Examples & Types


Chapter 12 / Lesson 4

An infinite series is the sum of terms in an infinitely long sequence, but taking the sum of terms in a finite portion of the sequence is called a partial sum. Explore these two concepts through examples of five types of series: arithmetic, geometric, harmonic, alternating harmonic, and telescopic.

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