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(Solved): Find a power series representation for the function. f(x)=(1+5x)2x)f(x)=n=0( Determi ...

$Find a power series representation for the function. \[ \begin{array}{r} \left.f(x)=\frac{x}{(1+5 x)^{2}}\right) \\ f(x)=\sum$

Find a power series representation for the function.

f (x) = \frac{x}{( 1 + 5 x ) ^{2}}) f (x) = ?_{n = 0}^{?} (

Determine the radius of convergence,

R

.

R =

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The power series of is defined as:

for ....(eq-1)

By using the known power series and replace method, solve the problem.

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