Divergence Test For Series - Calculus 2

This calculus 2 video tutorial provides a basic introduction into the divergence test for series. To perform the divergence test, take the limit as n goes to infinity for the sequence An. If the limit doesn't equal, then the series diverges. If the limit equals 0, the series may converge or it may divergence. Examples and practice problems include the analysis of a geometric series and the harmonic series using the divergence test.

Improper Integrals:

Converging & Diverging Sequences:

Monotonic & Bounded Sequences:

Absolute Value Theorem - Sequences:

Squeeze Theorem - Sequences:

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Geometric Series & Sequences:

Introduction to Series - Convergence:

Divergence Test For Series:

Harmonic Series:

Telescoping Series:

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Integral Test For Divergence:

Remainder Estimate - Integral Test:

P-Series:

Direct Comparison Test:

Limit Comparison Test:

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Calculus Final Exam and Video Playlists:

Full-Length Videos and Worksheets:

[victormai]

Thanks for making the video dark so I can peacefully cry myself to sleep while watching

[EMPujols]

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[ginamaccia]

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[felixcat]

Thanks for posting. I can see why this is used in statistics to prove or disprove the results of a set of data.

[karolinavalentina]

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[DiegoE]

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[guffbear]

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[jasminehurtado]

This was beyond helpful. How, why. Why don’t professors teach it this simply.

[GitNat]

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[JnSubli]

Do we have lectures for lim n→∞ aₙ ≠ 0 for oscillating transcedental functions such as: sin(n); 5+sin(n); sin(n)+cos(5n); f(n)*sin(n)?
Is this the only way Sum(|aₙ|, ∞, ∞+∞) / Sum( aₙ, ∞, ∞+∞) ≠ 2 to prove if series will diverge or undefined?

[steff.y]

Hi. How do you know when to use divergence test? Since one the definition of series is lim as n approaches infinity of Sn be a real number, then it is convergent?

[sezfx]

the video are much helping me in calculus.tq sir

[scitwi]

04:20 So what is the turning point for the terms of the sum before they blow up? Because that would be a better test.
For example, in the harmonic series, the terms go smaller and smaller (so the limit of the sequence of terms is 0, because they eventually shrink to 0 and stop piling up), but it seems that they don't shrink fast enough to not blow up the entire sum. On the other hand, in the geometric series (for `|r| < 1`) the terms also shrink to 0 eventually, but they do it fast enough so that the entire sum doesn't blow up. So what's the "speed limit" for those terms below which the series will converge, and as soon as they reach that value, it would blow up?

[lukaderetic]

such a good video me from high school understood everzthing much clearer than bz reading so many papers

[T-She-Go]

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[Rangerkidx]

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[arandomguymarra]

Your videos are always really helpful. Thank you.

[AC-tnit]

Wait so can we just use l’hopitals? It seems consistent with the answers

[nostalgiacademy]

I am highly confused as to why he multiplied the top and bottom by 1/n. He doesn't explain it at all and maybe its something I should know but it seems like that step comes from absolutely nowhere. Any help understanding???