Expand g(x) as indicated and specify the values of x for which the expansion is valid.

g(x) = (b+x)^(-1) in powers of x-a, a is not equal to -b.

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- May 19th 2010, 08:32 PMWartonMortonseries and validity
Expand g(x) as indicated and specify the values of x for which the expansion is valid.

g(x) = (b+x)^(-1) in powers of x-a, a is not equal to -b. - May 19th 2010, 09:33 PMques
- May 20th 2010, 05:07 AMWartonMorton
sumation from k=0 to inf of (-1)^k * k! * (b+x)^[(-1)(k+1)] * (x-a)

valid from (0,1/(b+a)] - May 20th 2010, 06:23 AMques
Sorry, that is not right ! From where do you have b+x as well as x-a ? What are the steps that you used to obtain the above step ?

You have $\displaystyle 1/(b+x)$

Step 1 :- What do you have after making the necessary substitutions as explained by my hint? Remember that you want it as powers of x-a.

Step 2 :- How do you expand $\displaystyle 1/(1+y)$ ? In this problem,what do you have in place of y ?

Later we can discuss the validity of convergence. - May 20th 2010, 06:32 AMWartonMorton
sorry don't know how to apply the hint.

- May 20th 2010, 07:03 AMques
- May 21st 2010, 06:10 AMques