Alternate Series Estimation Theorem

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This calculus 2 video tutorial provides a basic introduction into the alternate series estimation theorem also known as the alternate series remainder. It explains how to estimate the sum of the infinite series correct to three decimals places by calculating the number of terms needed by using the remainder estimate theorem.

Integral Test For Divergence:

Remainder Estimate - Integral Test:

P-Series:

Direct Comparison Test:

Limit Comparison Test:

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Alternating Series Test:

Alternate Series Estimation Theorem:

Absolute & Conditional Convergence:

The Ratio Test:

The Root Test:

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Series Tests - Practice Problems:

Taylor & Maclaurin Polynomials:

Taylor's Remainder Theorem:

Power Series - Interval Convergence:

Power Series - Derivatives & Integrals:

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Calculus Final Exam and Video Playlists:

Full-Length Videos and Worksheets:

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My calc II professor never covered this but is putting it on our homework and quizzes, and probably our exam too. So glad to see OCT has covered this topic!

Relaxed_lol

Thank you so much, besides the errors which were annoying and which I had to read through the comments to figure out, this video was very helpful. I had no clue how to do these types of problems and I have a midterm tomorrow, but now I think I understand how to do them!

matthewmoore

The signs should have flipped.

Many people have noticed this, and the general question may be.
How did OCT still get the correct answer despite this mistake, and what exactly happened?

The issue appears to be, the value of the remainder was plugged into the inequality, as if Rn = 0.0001
Remember it was not originally, the remainder naturally needs to be LESS than 0.0001 to be accurate to four decimal places.

So the inequality should have been set out with Rn <= An+1 <= 0.0001
Then the signs would certainly have flipped, as others have mentioned.

This would leave us with n >= correct answer

rmdir

I'm not gonna lie, I probably now have the chance of passing bc of you <3 YOU DESERVE A NOBEL PRICE FOR THIS

s.siddikaaa

taking the inverse of an inequality at 5:25 should flip the sign since they are both the same sign

niche

Why wasn't the direction of sign <= changed after their exponent was -1, I didn't get =/ 9:48

ferhat_ee-

Professor Organic Chemistry Tutor, thank you for another exceptional video/lecture on the Alternate Series Estimation Theorem in Calculus Two. I will review this topic for a clear and deep understanding of the Alternate Series Estimation Theorem and its error estimation. This is an error free video/lecture on YouTube TV with the Organic Chemistry Tutor.

georgesadler

This comment section points out so many errors in this video that im scared to watch the video😂

Marcosss--years-ago

You have incorrect calculations in 2 steps. First, a(n+1) must be less than 0.001. Second, when you raise both sides to the negative 1 power, or taking the reciprocal of both sides, you must invert the inequality sign. You missed the inequality sign twice, so your answer is correct, but that doesn't make your argument valid.

pto

You should have flipped the less than or equal to sign for a greater than or equal to sign when adding "to the power of minus one" on both sides

belenseoane

How would you go about this if you were not allowed a calculator?

artemis

So, why aren't we flipping the inequality sign whenever we take the inverse? we know that both values have to be positive

nicholasmaloof

In Maclaurin expansion of Sinx, find the remainder term after 3 term and find the value of θ ?

syedmdabid

I am confused, when trying to prove 1/n^2 is convergent, you cannot perform divergence test.. the divergence test only confirms if it is divergent if it is not equal to 0 and is inconclusive otherwise. I'm not sure how that can be applied in this problem unless someone wants to inform me on something I'm missing?

conintava