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Hey, here's is my problem as the exam states it:

A) Write out the first four non-zero terms of the Maclaurin Series for [tex]F(x) = (1+X^{7})^{-4}[/tex] Give all of the coefficients in exact form, simplified as much as possible.

B) Find the exact value of the 21st order derivative of [tex]F(x) = (1+X^{7})^{-4}[/tex] evaluated at x=0

I can not figure out an efficient(or simple) way to find the expansion of the given function. At first I tried using the known series 1/(1-X) = [tex]\sum X^{n}[/tex]

I replaced X in the equality with -X^7 to get [tex]\sum (-1)^{n}X^{7n}[/tex]

After this though, I'm lost. Apparently I'm not allowed to just multiply the general term by 1/(1+X^7)^3. So I've no idea what to do. :(

Hopefully the solution to A simplifies the solution to B

A) Write out the first four non-zero terms of the Maclaurin Series for [tex]F(x) = (1+X^{7})^{-4}[/tex] Give all of the coefficients in exact form, simplified as much as possible.

B) Find the exact value of the 21st order derivative of [tex]F(x) = (1+X^{7})^{-4}[/tex] evaluated at x=0

I can not figure out an efficient(or simple) way to find the expansion of the given function. At first I tried using the known series 1/(1-X) = [tex]\sum X^{n}[/tex]

I replaced X in the equality with -X^7 to get [tex]\sum (-1)^{n}X^{7n}[/tex]

After this though, I'm lost. Apparently I'm not allowed to just multiply the general term by 1/(1+X^7)^3. So I've no idea what to do. :(

Hopefully the solution to A simplifies the solution to B

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