LIM (1 / 2 + 1 / 2 ^ 2... + 1 / 2 ^ n) / (1 / 3 + 1 / 3 ^ 2... 1 / 3 ^ n) for limit LIM (1 / 2 + 1 / 2 ^ 2... + 1 / 2 ^ n) / (1 / 3 + 1 / 3 ^ 2... 1 / 3 ^ n) for limit
Original formula = LIM (n - > ∞) {[(1 / 2) (1-1 / 2 ^ n) / (1-1 / 2)] / [(1 / 3) (1-1 / 3 ^ n) / (1-1 / 3)]}
=[(1/2)/(1-1/2)]/[(1/3)/(1-1/3)]
=2.
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