Question

Which of the following are true statements (indicate all that apply)? If \sum_{n=0}^{\infty} |a_n||x - x_0|^n converges, then \sum_{n=0}^{\infty} a_n (x - x_0)^n converges. If \sum_{n=0}^{\infty} a_n (x - 5)^n converges when x = 2, then it also converges when x = 7. If \sum_{n=0}^{\infty} a_n (x - 5)^n converges when x = 2, then it might be divergent when x = 8. If \sum_{n=0}^{\infty} a_n (x - 5)^n converges when x = 2, then it might be convergent when x = 8. If \sum_{n=0}^{\infty} a_n (x - x_0)^n converges, then \sum_{n=0}^{\infty} |a_n||x - x_0|^n converges.

          Which of the following are true statements (indicate all that apply)?
If \sum_{n=0}^{\infty} |a_n||x - x_0|^n converges, then \sum_{n=0}^{\infty} a_n (x - x_0)^n converges.
If \sum_{n=0}^{\infty} a_n (x - 5)^n converges when x = 2, then it also converges when x = 7.
If \sum_{n=0}^{\infty} a_n (x - 5)^n converges when x = 2, then it might be divergent when x = 8.
If \sum_{n=0}^{\infty} a_n (x - 5)^n converges when x = 2, then it might be convergent when x = 8.
If \sum_{n=0}^{\infty} a_n (x - x_0)^n converges, then \sum_{n=0}^{\infty} |a_n||x - x_0|^n converges.

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Which of the following are true statements (indicate all that apply)?
If ∑n=0^∞ |an||x - x0|^n converges, then ∑n=0^∞ an (x - x0)^n converges.
If ∑n=0^∞ an (x - 5)^n converges when x = 2, then it also converges when x = 7.
If ∑n=0^∞ an (x - 5)^n converges when x = 2, then it might be divergent when x = 8.
If ∑n=0^∞ an (x - 5)^n converges when x = 2, then it might be convergent when x = 8.
If ∑n=0^∞ an (x - x0)^n converges, then ∑n=0^∞ |an||x - x0|^n converges.

Added by Joseph H.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Adi S

11/21/2022

Step 1

If the series \(\sum_{n=0}^{\infty} |a_n||(x-x_0)^n\) converges, then by the comparison test, the series \(\sum_{n=0}^{\infty} a_n(x-x_0)^n\) also converges. Show more…

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Which of the following are true statements (indicate all that apply)? If sum_(n=0)^(infty ) |a_(n)||x-x_(0)|^(n) converges, then sum_(n=0)^(infty ) a_(n)(x-x_(0))^(n) converges. If sum_(n=0)^(infty ) a_(n)(x-5)^(n) converges when x=2, then it also converges when x=7. If sum_(n=0)^(infty ) a_(n)(x-5)^(n) converges when x=2, then it might be divergent when x=8. If sum_(n=0)^(infty ) a_(n)(x-5)^(n) converges when x=2, then it might be convergent when x=8. If sum_(n=0)^(infty ) a_(n)(x-x_(0))^(n) converges, then sum_(n=0)^(infty ) |a_(n)||x-x_(0)|^(n) converges. Which of the following are true statements (indicate all that apply)? If L=o|an|x - xo|" converges, then L=o an(x -xo)" converges If =o an( - 5 converges when = 2, then it also converges when = 7. If =o an ( -- 5) converges when = 2, then it might be divergent when = 8. If L=o anx-xo converges, then =o|an||x-xo| converges.

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Transcript

00:03 Assume that 0 less than of a .n and 0 less than of bn.

00:12 Then which of the following statement is true? so it is given that if you find out the ratio of a .n divided by of bn and it is greater than 1.

00:33 Now the sequence an is greater than of bn.

00:44 So, a .n converges so that bn converges, you can say that same thing.

00:56 If a .n converges, then bn also converges.

01:01 So we can say that that a .n divided by bn is approximately equal to 0.

01:13 That means bn is approximately equal to of a .n.

01:19 So we need to take the constant value, that is of 3 less than a .n divided by bn less than of 17.

01:31 So we can write down that summation n is equal to 1 to k of a .m is less than of 2 .3 .000.

01:41 So then the series bn is converges.

01:49 So we can say that a bn is less than of a .n.

01:57 So option c is correct.

02:04 So in this way you can solve this problem.

02:10 Now in the next problem, next problem we can say that, assume that the series a .n is a real number and here bn is given here is of a .n.

02:32 If a .n is greater than equal to 0 and of 0 if a .n is less than 0.

02:44 Now and another thing cn is given here 0 if a .n greater than equal to 0 and this one a .n if a .n.

02:59 If a .n.

03:01 Is of less than 0...

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