Question

(1 point) Consider the series $sum_{n=1}^{infty} a_n$ where $a_n = (-1)^{n+9} frac{1}{n^6}$. Find the sum of the first four terms of the series. $s_4 = $ (Remember that you can make Webwork do your calculations for you! For example, you can write 1 + 2 + 3 + 4 instead of writing 10.) Using the alternating series error estimation theorem, find a bound for the magnitude of the error in the above estimation. The absolute value of the difference between $s_4$ and the entire sum of the series is at most: Using your above answers, the value of the entire sum is between $s_4$ and what other NUMBER (again, you can make Webwork do your calculations for you!)? The sum is between $s_4$ and:

          (1 point) Consider the series $sum_{n=1}^{infty} a_n$ where $a_n = (-1)^{n+9} frac{1}{n^6}$.
Find the sum of the first four terms of the series.
$s_4 = $
(Remember that you can make Webwork do your
calculations for you! For example, you can write 1 + 2 + 3 + 4 instead of writing 10.)
Using the alternating series error estimation theorem, find a bound for the magnitude of
the error in the above estimation.
The absolute value of the difference between $s_4$ and the entire sum of the series is at
most:
Using your above answers, the value of the entire sum is between $s_4$ and what other
NUMBER (again, you can make Webwork do your calculations for you!)?
The sum is between $s_4$ and:

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$(1 point) Consider the series sumn=1^infty an where an = (-1)^n+9 frac1n^6. Find the sum of the first four terms of the series. s4 = (Remember that you can make Webwork do your calculations for you! For example, you can write 1 + 2 + 3 + 4 instead of writing 10.) Using the alternating series error estimation theorem, find a bound for the magnitude of the error in the above estimation. The absolute value of the difference between s4 and the entire sum of the series is at most: Using your above answers, the value of the entire sum is between s4 and what other NUMBER (again, you can make Webwork do your calculations for you!)? The sum is between s4 and:$

Added by Shelly M.

Calculus: Early Transcendentals

James Stewart 8th Edition

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Solved by Expert William Semus

04/15/2022

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Consider the series sum_{n=1}^{infinity} a_n where a_n = (-1)^{n+9} 1/n^6. Find the sum of the first four terms of the series. s_4 = (Remember that you can make Webwork do your calculations for you! For example, you can write 1 + 2 + 3 + 4 instead of writing 10.) Using the alternating series error estimation theorem, find a bound for the magnitude of the error in the above estimation. The absolute value of the difference between s_4 and the entire sum of the series is at most: Using your above answers, the value of the entire sum is between s_4 and what other NUMBER (again, you can make Webwork do your calculations for you!)? The sum is between s_4 and:

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00:01 So in this question, they say we're going to consider the series sum from n equals 1 to infinity of a sub n, where a sub n is equal to negative 1 being raised to the power of n plus 9 times 1 over end of the 6th.

00:15 The first thing we want to do is we want to find the sum of the first four terms of the series.

00:23 So let's see.

00:24 If i have n equals 1, i'm getting negative 1 to the 10th power, that's positive 1 ,000, 1 times 1 over 1 to the 6th, that's just 1.

00:39 Then when it is 2, i'm getting negative 1 to the 11th power, so i get minus 1 over 2 to the 6th.

00:51 Then my next term is plus 1 over 3 to the 6th, and then it's minus 1 over 4 to the 6th.

01:04 Okay, so all i did is plug one in for n, then plug in two for n, plug in three for n, plug in four for n, and then we take that sum.

01:17 Now, if you want a value for that, okay, now it looks like you can write that in your answer here if you want.

01:27 It says you can write one plus two plus three plus four instead of writing 10.

01:32 So you could just write that 1 minus 1 over 2 to the 6th plus 1 over 3 to the 6th minus 1 over 4 to the 6th.

01:42 And that should be okay.

01:43 But if you did want the actual value for that, 1 minus 1 over 2 to 6th plus 1 over 3 to the 6th minus 1 over 4 to the 6th.

02:03 I don't know if this will convert to a fraction or not.

02:06 It won't, but 0 .985...

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