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konstantin123 [22]
2 years ago
13

Please help me with this

Mathematics
1 answer:
maria [59]2 years ago
6 0

Answer:

I think the answer is positive 8

Step-by-step explanation:

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Find a power series representation for the function. (Assume a>0. Give your power series representation centered at x=0 .)
melamori03 [73]

Answer:

Step-by-step explanation:

Given that:

f_x = \dfrac{x^2}{a^7-x^7}

= \dfrac{x^2}{a^7(1-\dfrac{x^7}{a^7})}

= \dfrac{x^2}{a^7}\Big(1-\dfrac{x^7}{a^7} \Big)^{-1}

since  \Big((1-x)^{-1}= 1+x+x^2+x^3+...=\sum \limits ^{\infty}_{n=0}x^n\Big)

Then, it implies that:

\implies  \dfrac{x^2}{a^7} \sum \limits ^{\infty}_{n=0} \Big(\Big(\dfrac{x}{a} \Big)^{^7} \Big)^n

= \dfrac{x^2}{a^7} \sum \limits ^{\infty}_{n=0} \Big(\dfrac{x}{a} \Big)^{^{7n}}

= \dfrac{x^2}{a^7} \sum \limits ^{\infty}_{n=0} \Big(\dfrac{x^{7n}}{a^{7n}} \Big)}

\mathbf{=  \sum \limits ^{\infty}_{n=0} \dfrac{x^{7n+2}}{a^{7n+7}} }}

7 0
2 years ago
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