"Expand the function" power series questions

1)What does it mean? The problem is asking you to write 18+7x\displaystyle \dfrac{1}{8+7x} in the form given. What are you not understand there?

You know (or should know) that 11x=1+x+x2+x3+x4...\displaystyle \dfrac{1}{1-x}=1 +x+ x^2 + x^3 + x^4 .... Do NOT believe what I just said! Do the division yourself and see that my formula is correct. Now basically do the same for 18+7x\displaystyle \dfrac{1}{8+7x}.
18+7x\displaystyle \dfrac{1}{8+7x} = (18)11+78x\displaystyle (\dfrac{1}{8})\frac{1}{1+\frac{7}{8}x}=(18)1178x\displaystyle (\dfrac{1}{8})\frac{1}{1-\frac{-7}{8}x}.
Continue from here.
 
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