Can someone help me develop the mac Laurin series of (x-x^2)/(1+3)^3 and find An?

Question

Can someone help me develop the mac Laurin series of  (x-x^2)/(1+3)^3 and find An?

hartnn · Answer

so, is it really  (x-x^2)/(1+3)^3 ? 
that just comes out to  (x-x^2)/64
....
or have you done any typing error?

anonymous · Answer

That's what is written

hartnn · Answer

for Maclauren series, you basically find 
f(0),f'(0), f" (0) ....and so on...
could you find those ?

anonymous · Answer

$$(x-x^2)/(1+x)^3$$

anonymous · Answer

It's a series of form  $$\sum_{n=0}^{\infty} a _{n}x ^{n}$$

anonymous · Answer

But I'm not sure how to procede

hartnn · Answer

http://mathworld.wolfram.com/MaclaurinSeries.html

hartnn · Answer

you basically need these
f(0),f'(0), f" (0) ....and so on...
cold you find f'(x) first?

anonymous · Answer

I Use the quotient rule over and over ?

hartnn · Answer

yes, i guess thats the only way...the hard way....

hartnn · Answer

but you'll plug in x=0, that simplifies things alot...

anonymous · Answer

Well it's to find the nth term...I'm not sure how to procede though .. I mean in an easier way to get to the nth term

hartnn · Answer

i couldn't think of easier way......just quotient rule everytime you differentiate...

anonymous · Answer

Ive been trying but I can't seem to make it there ..  I've been able to solve others but Maclaurin series are tough for me 
Would you know any type of .. ''Maclaurin series for dummies'' type of sites? lol

hartnn · Answer

lol ok...have you tried khan academy ? i haven't used it, but i hear its good https://www.khanacademy.org/math/calculus/sequences_series_approx_calc/maclaurin_taylor/v/maclauren-and-taylor-series-intuition

anonymous · Answer

Thanks a Lot! I'll give it a shot .. And keep practicing .. Thanks Again!

hartnn · Answer

cool, welcome ^_^