Use Strategy D13 from Unit D3 to determine whether each of the following series converges. Name...

 

Transcribed Image Text:

Use Strategy D13 from Unit D3 to determine whether each of the following series converges. Name any results or rules that you use. You may use the basic series listed in Theorem D33 from Unit D3. (a) n=1 8 2n3+5 4n3-1 n23n (b)(n+4)n! (c) Σ n=1 8 3n2-4 cos n 4n4+1 (d)(-1)+12 3n3-2 111 Strategy D13 To determine whether a series an is convergent or divergent, do the following. 1. If you think that the sequence of terms (an) is non-null, then try the Non-null Test. 2. If an has non-negative terms, then try one of these tests. Basic series Isan a basic series, or a combination of these? Comparison Test Is an bn, where bn is convergent, or an ≥ bn ≥ 0, where bn is divergent? Limit Comparison Test Does an behave like bn for large n (that is, does an/bnL0), where Σbn is a series that you know converges or diverges? Ratio Test Does an+1/an → 11? 3. If an has infinitely many positive and negative terms, then try one of these tests. Absolute Convergence Test Islan| convergent? (Use step 2.) Alternating Test Is an = (-1)+1bn, where (bn) is non-negative, null and decreasing? Re Use Strategy D13 from Unit D3 to determine whether each of the following series converges. Name any results or rules that you use. You may use the basic series listed in Theorem D33 from Unit D3. (a) n=1 8 2n3+5 4n3-1 n23n (b)(n+4)n! (c) Σ n=1 8 3n2-4 cos n 4n4+1 (d)(-1)+12 3n3-2 111 Strategy D13 To determine whether a series an is convergent or divergent, do the following. 1. If you think that the sequence of terms (an) is non-null, then try the Non-null Test. 2. If an has non-negative terms, then try one of these tests. Basic series Isan a basic series, or a combination of these? Comparison Test Is an bn, where bn is convergent, or an ≥ bn ≥ 0, where bn is divergent? Limit Comparison Test Does an behave like bn for large n (that is, does an/bnL0), where Σbn is a series that you know converges or diverges? Ratio Test Does an+1/an → 11? 3. If an has infinitely many positive and negative terms, then try one of these tests. Absolute Convergence Test Islan| convergent? (Use step 2.) Alternating Test Is an = (-1)+1bn, where (bn) is non-negative, null and decreasing? Re

Answer rating: 100% (QA)

Lets analyze each series using Strategy D13 from Unit D3 to determine whether they converge or diver... View the full answer