Why Is My Series Error Estimate Calculation Incorrect?

[Umar]

Hey, I have a quick question here from my assignment. I thought it did it right the first time but I got the wrong answer, and I can't possibly seem to find anything wrong with my solution. Any ideas?

Link to Question:

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So, I started by solving the integral by following the Remainder Estimate for the Integral Test, and got 1/(6(n^6)). Again, I'm pretty sure there is no mistake in getting to that result (bounds: n to infinity, so I took the limit as t approaches infinity and replaced the upper bound with t).

I came to the following inequality:

1/(6(n^6)) < 0.0001

Solving this inequality, I got n = 3, which seems too low, but I got a half mark for some reason (lol...)

Can anyone please try and point out anything I'm doing wrong, probably with the inequality? Thanks!

 

[jvicens]

Dear student,

Thank you for reaching out with your question. It's great to see that you are taking the time to double check your work and seek clarification when you encounter difficulties.

First of all, I commend you for correctly using the Remainder Estimate for the Integral Test in solving the given integral. From what you have described, it seems like you have followed the steps correctly and arrived at the right result.

However, I do see an error in your inequality. When solving for n, you should have taken the inverse of both sides of the inequality, so the correct solution would be n > 3, rather than n = 3. This makes more sense, since the value of n should be greater than 3 in order for the inequality to hold true.

I would recommend revisiting your steps and double checking your work, especially when solving for inequalities. It's always a good idea to go through your work again to catch any small mistakes that may have been overlooked.

I hope this helps and good luck with your assignment! Keep up the good work in your studies.