CK-12-Calculus

8.1. Sequences http://www.ck12.org Y 3 (x) = 1 + ∫x − 1 t ( 5 8 + t^2 4 + t^4 8 ) dt Y 3 (x) = 1 + ( 5 t 2 16 + t^4 16 + t^6 48 ...

http://www.ck12.org Chapter 8. Infinite Series 9. { 6 n 2 en } Let{an}be a sequence such that limn→+∞|an|=0. Show that limn→+∞a ...

8.2. Infinite Series http://www.ck12.org 8.2 Infinite Series Learning Objectives Demonstrate an understanding of series and the ...

http://www.ck12.org Chapter 8. Infinite Series u 1 +u 2 +u 3 +u 4 +.... A shorthand notation for an infinite series is to use si ...

8.2. Infinite Series http://www.ck12.org Convergence/Divergence of Series Let∑∞k= 1 ukbe an infinite series and let{sn}be the se ...

http://www.ck12.org Chapter 8. Infinite Series sn=^109 ( 1 − 101 n) Now we find the limit of both sides: n→lim+∞sn=nlim→∞^109 ( ...

8.2. Infinite Series http://www.ck12.org Example 5 Determine if the series 7+^78 + 872 + 873 +...+ 8 i^7 − 1 +...converges or di ...

http://www.ck12.org Chapter 8. Infinite Series Sn= n k∑= 1 ( 2 k− 2 k+ 1 ) = ( 2 1 − 2 1 + 1 ) + ( 2 2 − 2 2 + 1 ) + ( 2 3 − 2 3 ...

8.2. Infinite Series http://www.ck12.org Determine if∑∞k= (^1) k−^83 converges or diverges. Solution Using thenth-Term Test, lim ...

http://www.ck12.org Chapter 8. Infinite Series Theorem If∑∞k= 1 ukconverges, then∑∞k= 1 uk+(u 1 +u 2 +...+um)is also convergent. ...

8.2. Infinite Series http://www.ck12.org Suppose∑∞k= 1 Ukis a convergent series and∑∞k= 1 Vkis a divergent series. Explain why∑ ...

http://www.ck12.org Chapter 8. Infinite Series 8.3 Series Without Negative Terms Learning Objectives Demonstrate an understandi ...

8.3. Series Without Negative Terms http://www.ck12.org If two fractions have the same numerator but different denominators, the ...

http://www.ck12.org Chapter 8. Infinite Series ... Intuitively, we can see that there is no bound on the sequence of partial sum ...

8.3. Series Without Negative Terms http://www.ck12.org The Integral Test Another useful test for convergence or divergence of an ...

http://www.ck12.org Chapter 8. Infinite Series Limit Comparison Test, Simplified Limit Comparison Test Another test we can use t ...

8.3. Series Without Negative Terms http://www.ck12.org Write an example of a sequence that is not nondecreasing. Suppose{Sn}is ...

http://www.ck12.org Chapter 8. Infinite Series 8.4 Series With Odd or Even Negative Terms Learning Objectives Demonstrate an un ...

8.4. Series With Odd or Even Negative Terms http://www.ck12.org The Alternating Series Test As its name implies, theAlternating ...

http://www.ck12.org Chapter 8. Infinite Series Suppose an alternating series satisfies the conditions of the Alternating Series ...