Site Map - A full listing of all the content on the site as well as links to the content. We can in turn use the upper and lower bounds on the series value to actually estimate the value of the series. Select this option to open a dialog box. patrickJMT 156,022 views 9:48 Alternating series error estimation - Duration: 9:18.

Example 1 Â Using Â to estimate the value of . In this case weâ€™ve used the ratio test to show that Â is convergent.Â To do this we computed and found that . The function is , and the approximating polynomial used here is Then according to the above bound, where is the maximum of for . Now that weâ€™ve gotten our second series letâ€™s get the estimate. Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â So, how good is it?Â Well we know that, Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â will be an upper bound for

patrickJMT 318,155 views 11:21 Alternating Series 1b - Estimating the Remainder - Duration: 7:32. Krista King 13,943 views 12:03 Absolute Convergence, Conditional Convergence and Divergence - Duration: 11:21. Once on the Download Page simply select the topic you wish to download pdfs from. DrPhilClark 38,394 views 9:33 A Proof for the Existence of God - Duration: 2:41.

But the big takeaway here is that the magnitude of your error is going to be no more than the magnitude of the first term that you're not including in your Working... In the mean time you can sometimes get the pages to show larger versions of the equations if you flip your phone into landscape mode. Calculus II (Notes) / Series & Sequences / Estimating the Value of a Series [Notes] [Practice Problems] [Assignment Problems] Calculus II - Notes Parametric Equations and Polar Coordinates Previous Chapter

Note If the series is strictly decreasing (as is usually the case), then the above inequality is strict. Loading... It's going to be different depending on whether the first term is negative or positive, and we're going to have to introduce the idea of absolute value there, the magnitude. Plus .04 gets us to .83861 repeating, 83861 repeating.

Now, since Â we also know that When using the comparison test it is often the case that the bn are fairly nice terms and that we might actually And just like that, just a calculation we're able to do by hand, we were able to come up with a pretty good approximation for S. Actually, this logic right over here is the basis for the proof of the alternating series test. Watch Queue Queue __count__/__total__ Find out whyClose Alternating Series - Error Estimation patrickJMT SubscribeSubscribedUnsubscribe593,028593K Loading...

Notice that this method did require the series terms to be positive, but that doesnâ€™t mean that we canâ€™t deal with ratio test series if they have negative terms.Â Often series You can access the Site Map Page from the Misc Links Menu or from the link at the bottom of every page. If Â is a decreasing sequence and Â then, Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â If Â is a increasing sequence then, Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Proof Both parts will need the following work so weâ€™ll do it first.Â Weâ€™ll Loading...

Sign in 113 6 Don't like this video? My Students - This is for students who are actually taking a class from me at Lamar University. Thus, we have But, it's an off-the-wall fact that Thus, we have shown that for all real numbers . We're going to start at n equals one, and go to infinity of negative one to the n plus one over n squared, which is going to be equal to ...

I'll do that same pink color. Mr. Since , the question becomes for which value of is ? What is the maximum possible error of the th Taylor polynomial of centered at on the interval ?

Integral Test Recall that in this case we will need to assume that the series terms are all positive and will eventually be decreasing.Â We derived the integral test by using That maximum value is . As weâ€™ll soon see if we can get an upper and lower bound on the value of the remainder we can use these bounds to help us get upper and lower All of this other stuff, I don't want even the brackets to end.

Ian Aston 2,873 views 4:59 Power Series Representation of Functions - Duration: 10:10. And the big takeaway from here ... Thus 9 terms are required to be within of the true value of the series. One way to get an approximation is to add up some number of terms and then stop.

You should see a gear icon (it should be right below the "x" icon for closing Internet Explorer). Note for Internet Explorer Users If you are using Internet Explorer in all likelihood after clicking on a link to initiate a download a gold bar will appear at the bottom How close will the result be to the true answer? It's bounded from above at 1/25, which is a pretty good sense that hey, this thing is going to converge.

You can also send feedbackVery dissatisfiedVery satisfied Language: English Content location: United States Restricted Mode: Off History Help Loading... Note If you actually compute the partial sums using a calculator, you will find that 7 terms actually suffice. Generated Sat, 15 Oct 2016 06:56:46 GMT by s_wx1131 (squid/3.5.20) ERROR The requested URL could not be retrieved The following error was encountered while trying to retrieve the URL: http://0.0.0.9/ Connection Algebra [Notes] [Practice Problems] [Assignment Problems] Calculus I [Notes] [Practice Problems] [Assignment Problems] Calculus II [Notes] [Practice Problems] [Assignment Problems] Calculus III [Notes] [Practice Problems] [Assignment Problems] Differential Equations [Notes] Extras

Included in the links will be links for the full Chapter and E-Book of the page you are on (if applicable) as well as links for the Notes, Practice Problems, Solutions Loading... So, letâ€™s start with a general discussion about the determining how good the estimation is.Â Letâ€™s first start with the full series and strip out the first n terms.Â Â Â Â Â Â Â (1)