6. Find A and B such that for all i > 2 1 A i2 + 5i + 6 i+2 i +3' Mol and use this identity to express the partial sum s, = 1/(2² + 5i +6) of the series 1 22+5i + 6 n21 as a telescoping sum. Use this telescoping sum to show first that the series is convergent, and find its sum.
6. Find A and B such that for all i > 2 1 A i2 + 5i + 6 i+2 i +3' Mol and use this identity to express the partial sum s, = 1/(2² + 5i +6) of the series 1 22+5i + 6 n21 as a telescoping sum. Use this telescoping sum to show first that the series is convergent, and find its sum.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![**Problem Statement:**
6. Find \( A \) and \( B \) such that for all \( i \geq 2 \)
\[
\frac{1}{i^2 + 5i + 6} = \frac{A}{i+2} + \frac{B}{i+3}
\]
and use this identity to express the partial sum
\[
s_n = \sum_{i=1}^{n} \frac{1}{i^2 + 5i + 6}
\]
of the series
\[
\sum_{n \geq 1} \frac{1}{i^2 + 5i + 6}
\]
as a telescoping sum. Use this telescoping sum to show first that the series is convergent, and find its sum.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0ec25ffb-8aef-468b-ad53-a5caf8bbc7e2%2Ff9e03175-9029-4524-9d4e-4687d5b91c3f%2Fwntbxh_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
6. Find \( A \) and \( B \) such that for all \( i \geq 2 \)
\[
\frac{1}{i^2 + 5i + 6} = \frac{A}{i+2} + \frac{B}{i+3}
\]
and use this identity to express the partial sum
\[
s_n = \sum_{i=1}^{n} \frac{1}{i^2 + 5i + 6}
\]
of the series
\[
\sum_{n \geq 1} \frac{1}{i^2 + 5i + 6}
\]
as a telescoping sum. Use this telescoping sum to show first that the series is convergent, and find its sum.
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