Multiplication and Division of Power Series

Multiplication and Division of Power Series - Using Multiplication and Division of Power Series to derive Power Series Representations for other functions! Two examples are shown.
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Category:

Education

Tags:

• math
• calculus
• multiply
• divide
• power
• series
• representations
• multiplication
• division
• example
• taylor
• maclaurin
• justmathtutoring.com

[caligal2010]

Im scared to come across the day when even Patrick fails to help me understand a concept. I hope I never have to take that horrid class.

[patrickJMT]

@caligal2010 yes we can

[StrictVision]

i wish i found u earlier x.x

[patrickJMT]

@StrictVision spread the word, so that others will know : )

[FaiththeHairstylist]

Hmm, not sure I've seen this in my book. Is this just something for doing representation of a power series?

[patrickJMT]

@FaiththeHairstylist yep, just another way to produce new power series from old ones

[patrickJMT]

@mikeyagiela89 hahahhhahh, i think you would have still passed without me : )

but i am happy if i made your life at least a bit easier!

[mikeyagiela89]

I would have failed algebra2, precalc, calc, calc2, calc3, and diff eq without you. you're my hero

[ChronosRequiem]

Good!, l did not see so, thank you... you are dynamic.

[youspinmerightrounds]

@genrytov If you differentiate a function wrt x which has a term such as An x^n then you will find that the first term in the first derivative of the series is zero, so it's derivative starting at 1 is the same as starting at zero. Similarly the second derivative's first two terms are zero, so starting the sum at n=2 is the same as n=0. However, if the series is like An x^(n+r) this will not happen and you will have to start each series at zero.

[beckels730]

how would you find the first three nonzero terms in the series?

[AgentBlackX]

YOU ARE SUCHA BETTER TEACHER THAN MY CURRENT CALC PROFESSOR

[thangbanhbao]

I just noticed that writing with your LEFT hand is only useful when writing old chinese or japanese. With english writing from left to right it is HARD dont u think patrick =0

[robx0r]

I got (7/360)x^4 for the 3rd term.