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5. Consider the series below ∞ 1 n² + n n=1 1 (a) Use partial fraction decomposition to rewrite as the sum of two rational expressions. n²+n Show all steps in the partial fraction decomposition process. (b) Write out the first five partial sums, S₁ through S5. (Hint: Simplify each only as the sum of an integer and a unit fraction.)

5. Consider the series below ∞ 1 n² + n n=1 1 (a) Use partial fraction decomposition to rewrite as the sum of two rational expressions. n²+n Show all steps in the partial fraction decomposition process. (b) Write out the first five partial sums, S₁ through S5. (Hint: Simplify each only as the sum of an integer and a unit fraction.)

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.3: Geometric Sequences
Problem 82E
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Please solve the following calc 2 questiom (use calc 2 conceptes only) 

 

5. Consider the series below 1 n² + n 1 n²+n n=1 (a) Use partial fraction decomposition to rewrite as the sum of two rational expressions. Show all steps in the partial fraction decomposition process. (b) Write out the first five partial sums, S₁ through S5. (Hint: Simplify each only as the sum of an integer and a unit fraction.) (c) Use your work from part (b) to find the nth partial sum, Sn. (d) Use your work from part (c) to determine whether the infinite series converges or diverges. If it converges, find its sum.
Transcribed Image Text:5. Consider the series below 1 n² + n 1 n²+n n=1 (a) Use partial fraction decomposition to rewrite as the sum of two rational expressions. Show all steps in the partial fraction decomposition process. (b) Write out the first five partial sums, S₁ through S5. (Hint: Simplify each only as the sum of an integer and a unit fraction.) (c) Use your work from part (b) to find the nth partial sum, Sn. (d) Use your work from part (c) to determine whether the infinite series converges or diverges. If it converges, find its sum.
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