{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

sec11_5

# sec11_5 - ∞ ± n =1-1 n 1 n 1 Section 11.5.Alternating...

This preview shows pages 1–2. Sign up to view the full content.

11.5 Alternating Series 1. Alternating Series Test An alternating series is a series whose terms are alternately positive and negative. 1 - 1 2 + 1 3 - 1 4 + 1 5 - ... = n =1 ( - 1) n - 1 n In the form of a n = ( - 1) n - 1 b n , or a n = ( - 1) n b n where b n = | a n | . Theorem 1.1 (The Alternating Series Test) . If the alternating series n =1 ( - 1) n - 1 b n = b 1 - b 2 + b 3 - b 4 + b 5 - b 6 + ..., b n > 0 satisfies ( i ) b n +1 b n for all n ( ii ) lim n →∞ b n = 0 then the series is convergent. Example 1.1 (The Alternating Harmonic Series) . Determine whether or not the series converges or diverges. Explain.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ∞ ± n =1 (-1) n +1 n 1 Section 11.5.Alternating Series 2 Example 1.2. (problem 4) Test the series for convergence or divergence. 1 √ 2-1 √ 3 + 1 √ 4-1 √ 5 + 1 √ 6-... Example 1.3. (problem 11) Test the series for convergence or divergence. ∞ ± n =1 (-1) n +1 n 2 n 3 + 4 Example 1.4. (problem 15) Test the series for convergence or divergence. ∞ ± n =1 cos nπ n 3 / 4...
View Full Document

{[ snackBarMessage ]}

### Page1 / 2

sec11_5 - ∞ ± n =1-1 n 1 n 1 Section 11.5.Alternating...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online