Having the following series: &#x2212;<!-- − --> 1 2 </mfrac> + 1 6 <

babyagelesszj

babyagelesszj

Answered question

2022-07-13

Having the following series:
1 2 + 1 6 1 10 + 1 14 1 18 +
What is the easiest approach to find a general formula for this series?

Answer & Explanation

pompatzz8

pompatzz8

Beginner2022-07-14Added 11 answers

It is
n = 1 ( 1 ) n 2 ( 2 n 1 )
and this sum admit a closed form, in fact is the Taylor series of arctangent. So
n = 1 ( 1 ) n 2 ( 2 n 1 ) = 1 2 n = 1 ( 1 ) n 2 n 1 = 1 8 π .

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