Show that the ratio Test is inconclusive but the Root Test indicates convergence for the series

1/2 + 1/3^2 + 1/2^3 + 1/3^4 + 1/2^5 + ...

1/2 + 1/3^2 + 1/2^3 + 1/3^4 + 1/2^5 + ...

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