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For example

var('k x')
giac('normal(sum((1+(-1)^k)*x^k,k,0,inf))').sage()

-2/(x^2 - 1)

For example

var('k x')
giac('normal(sum((1+(-1)^k)*x^k,k,0,inf))').sage()

-2/(x^2 - 1)

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