How would one prove that the sum, from n=0 to infinite, of the alternating power series (-1)^n/[3^n*(2n+1)] equals Pi/[2(3)^.5]? I'm having some difficulty conceptualizing the process.
How would one prove that the sum, from n=0 to infinite, of the alternating power series (-1)^n/[3^n*(2n+1)] equals Pi/[2(3)^.5]? I'm having some difficulty conceptualizing the process.
Originally Posted by jallison88
How would one prove that the sum, from n=0 to infinite, of the alternating power series (-1)^n/[3^n*(2n+1)] equals Pi/[2(3)^.5]? I'm having some difficulty conceptualizing the process.
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I happen to know that, because it is arctangent series.
and also know that, because it is geometric series. But I do not see how to deal with both of them together.
How would one prove that the sum, from n=0 to infinite, of the alternating power series (-1)^n/[3^n*(2n+1)] equals Pi/[2(3)^.5]? I'm having some difficulty conceptualizing the process.
Look at the power series for , then let , and then Bob's your uncle.