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## Homework Statement

Consider the power series

Σanxn = 1+2x+3x2+x3+2x4+3x5+x6+…

in which the coefficients an=1,2,3,1,2,3,1,... are periodic of period p=3. Find the radius of convergence.

## Homework Equations

## The Attempt at a Solution

My attempt at a solution was to first state that the series was geometric as

*r*=x

In order for this series to converge, the absolute value of r must be less than 1.

|r|<1

Therefore |x|<1.

Based on this, the interval of convergence is (-1,1) and the radius is r=1.

Based on my solution, I did not take into account an.... If there is another solution I would need to take an into account to solve the radius of convergence please let me know.