g(x) = 2 / (1-x)^3 center c=0

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- January 11th 2010, 09:34 PMharveyopower series expansion
g(x) = 2 / (1-x)^3 center c=0

- January 11th 2010, 09:41 PMJhevon
- January 11th 2010, 10:11 PMharveyo
- January 12th 2010, 06:15 AMHallsofIvy
You haven't done

**anything**that jhevon suggested!

He suggested that you write out the power series for and differentiate**that**twice!

What is the power series for ?

(Hint: the sum of the geometric series is .) - January 15th 2010, 05:44 PMharveyo
power series

1/ 1-x = 1 + x +x^2 + x^3 ......

therefore

1/ (1-x)^2 = 1+ 2x +3x^2 +4x^3 ......

now

1/(1-x)^3 = 2 + 6x + 12x^2 .....

? - January 16th 2010, 07:58 AMawkward
- January 16th 2010, 02:56 PMJhevon
the left side of your third equation is incorrect. and when i said differentiate the power series for 1/(1 - x) i was talking about differentiating the expression behind the summation sign in , for , twice

or you can follow awkwards suggestion if you learned the negative binomial theorem