please andwer as if you were to submit The following series converges to a ratio

Question

please andwer as if you were to submit

The following series converges to a rational function in x for x in a certain interval F(x) = 1 - 3x + 3x2 + x3 - 3x4 + 3x5 + x6 - 3x7 + 3x8 + ..What is the interval of convergence? Give your answer using interval notation. If you need to use infinity, type INF. If there is only one point in the interval of convergence, the interval notation is [a]. For example, if 0 is the only point in the interval of convergence, you would answer with [0].The interval of convergence is

Explanation / Answer

F(x) = sum (-3x)^n = 1/(1+3x) (geometric series)

The convergences is for |-3x| < 1 => |x| < 1/3

The interval of convervence is (-1/3,1/3)

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