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I have a couple questions about the sums of geometric series.

One. So the formula for the sum is
But if my series starts at t(0), can I change the formula to

Two. If, in the series, there is a different pattern in the numerator than in the denominator, how can I solve it?
Such as: [x/2]+[(x^2)/4]+[(x^3)/8]...

Thank you.

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