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7.4.2: Sums of Infinite Geometric Series

7.4.2: Sums of Infinite Geometric Series

SOLVED:Use geometric series to show that (a) ∑k=0^∞(-1)^k x^k=(1)/(1+x) if -1<x<1 if 2<x<4 (b) ∑k=0^∞(x-3)^k=(1)/(4-x) if 2<x<4 (c) ∑k=0^∞(-1)^k x^2 k=(1)/(1+x^2) if -1<x<1

SOLVED:Use geometric series to show that (a) ∑k=0^∞(-1)^k x^k=(1)/(1+x) if -1<x<1 if 2<x<4 (b) ∑k=0^∞(x-3)^k=(1)/(4-x) if 2<x<4 (c) ∑k=0^∞(-1)^k x^2 k=(1)/(1+x^2) if -1<x<1

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