The sum of the geometric series for Xac-2 n[tex](n ~ 1) (~1)" I2"-2 for Ixl < 1 is (1 - x2)[/tex]. This is because the series is a summation of the terms (1/x2) multiplied by each power of x from 0 to n, and the sum of the series is the sum of the terms.
To calculate the sum of the geometric series for[tex]Xac-2 n (n ~ 1) (~1)" I2"-2 for Ixl < 1[/tex], we can use the formula for the sum of a geometric series. The sum of such a series is the sum of the terms (1/x2) multiplied by each power of x from 0 to n. Thus, the sum of the series is given by the formula S = (1/x2) ∑ xn, where n starts at 0 and goes to n. Substituting n = -2 and x = 1 gives us S = (1/1) ∑ 1-2, which simplifies to S = (1/1) (1 - 1-2) = (1 - 1-2) = (1 - x2). Hence, the sum of the series is (1 - x2).
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