Binomial series (KristaKingMath)

Learn how to use the binomial series to expand the function as a power series. Then state the radius of convergence of the power series.

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Hi, I’m Krista! I make math courses to keep you from banging your head against the wall. ;)

Math class was always so frustrating for me. I’d go to a class, spend hours on homework, and three days later have an “Ah-ha!” moment about how the problems worked that could have slashed my homework time in half. I’d think, “WHY didn’t my teacher just tell me this in the first place?!”

[akakoon]

Remember that each term in the series {3, 7, 11, ...} adds 4 to the previous term, so the term before (4n-1) in the numerator is (4n-5).  This term cancels with the (4n-5) in the denominator, leaving (4n-1) in the numerator.

[msokiedokie]

Thank you times a million seriously ! You're great and very very easy to understand ! Best explanation I've found so far

[kiraenigma]

integralCALC 14:10 what happend with (4n-5) in denominator? :S

[bbb-unhq]

at 10:24 If you look at (1-x)^.25 in the upper left
look at the x term
|-x| < 1 = R
= |x| < 1 = R
It gives you R  without a ratio test!

[URBIdaBAST]

Very helpful and clear. I had a problem with a letter constant, this didn't help very much, but still allowed me to understand the process.

[Dguy]

Hey did you forget about the 4n-5 in the denominator when solving for the radius of convergence? It seems to just disappear from your first line of multiplying the inverse to the second line where you are simplifying the factorial
Thanks!

[twelvemistymountains]

Hey thanks for the video, helped a lot ! At 16:20 though, when finding the limit value at n = ∞, I felt the factoring out of n was missing, and staying with n^(-1) so they zero off, and then 4/4 really is one. Someone could take that part too naively .. Thanks again you're great !

[peterhaulofu]

But where did the (4n-5) in the denominator disappear to?

[jessmarbongolto]

Hi ma'am what happened to the (4n-5)?

[mac]

This tutorial helps explain a lot. Your a star thank you.

[tiborsovilj]

14:10 what happend with (4n-5) in denominator? :S

[nicolereplogle]

Shouldn't the 11/4 be negative? (1/4-3)=-11/4, making that term positive? Thanks for uploading your videos, it's a lot of help!

[chrisgallon]

wait... what happened to the (4n-5) term on the righthand side?

[marketcycles]

great dear, u have a very clear voice, thank you so much

[cassied]

YouTube got me feeling like a Pokémon Trainer. “Krista King, I choose you” (except I am being trained 😂)

Krista King
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You evoke them at different times.

[helpdisc]

Krista the Queen math my question is for convergence the index of series must be negative...? ...can you explain it

[syedmdabid]

What-th term is 3 y z^2 in the expansion of (x+y+z)^3 ? (3 second)

[ThePukdurapuk]

Hi thank you for your videos, can you provide more examples and reviews for calculus part 2 (integration, application of integrals, series etc)?

[raunakbanerjee]

hey.
could you help me here.
i have a series 3C1 +7C1+... (4n-1)Cn... how do i sum it up?

[ananava]

you explain it so easy! thank you so much