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the series is (3^n x^n ) / (n+1)^2,

did the ratio test and found the radius of convergence to be the 1/3.

now for finding the interval of convergence I plug in -1/3 and 1/3 into x and find out if it converges or not

For 1/3, it converges due to p-series, 2>1.

But for -1/3 I know it converges but can see why? Any help here at this endpoint?