Use the sum of the first 10 terms to approximate the sum of...

Use the sum of the first 10 terms to approximate the sum of the series. (Round your answer to five decimal places.) $\sum_{n=1}^{\infty} \frac{1}{8 + n^5}$ Estimate the error. $R_{10} \leq \int_{10}^{\infty} \frac{1}{x^5} = $

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Transcript

00:02 Hello, welcome to this lesson.

00:04 In this lesson we'll use the 5, 10 times to estimate the summation n from 1 to infinity of 1 on 3 plus n to the power 5.

00:16 Okay, essentially we are looking at the estimation to 1 on 3 plus 10 to the power 5.

00:46 Okay, so let's use sl for this.

00:50 Let's have n, then we'd have 3 plus n to the power 5.

00:54 We'll have 1 on 3 plus n to the power 5.

01:00 Okay, so n start from 1 to 10, rounding it to 5 decimal places.

01:18 So here we have 3 plus, let's use power, actually let me use equals to.

01:26 So we'll have 3 plus power, then we'd have, this is the n value, to the power 5.

01:35 Okay, and now we can drag through to fill in for the others.

01:43 The next part, let's have 1 on these answers.

01:50 Okay, so let's also drag through to fill in.

01:57 Alright, and now looking at the summation n from 1 to 10, just as we have done, 1 on 3 plus n to the power 5, actually equals to, let's round this to 5 decimal places.

02:17 So we'll have round, and we are summing.

02:21 So we are summing from this side to that side.

02:27 Okay, then we provide the number of decimal places.

02:31 Okay, and this gives us, so the whole of this gives us 0 .28418.

02:43 And now the second part, we'll look at the arrow...

Question

Use the sum of the first 10 terms to approximate the sum of the series. (Round your answer to five decimal places.) $\sum_{n=1}^{\infty} \frac{1}{8 + n^5}$ Estimate the error. $R_{10} \leq \int_{10}^{\infty} \frac{1}{x^5} = $

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