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The first sum (let's denote it ) can be calculated in the following way:
.
On the other hand:
from where it is clear that
.
The value of can be calculated using the following integral
,
where the closed contour is chosen to go from to below the real axis and back above it. The only poles of the function under the integral are those of cotangent. Therefore . The final result is .
The second sum can be calculated in a similar way.
No, consecutive primes. The first one: 1st and 2nd primes, then 2nd and 3rd, then 3rd and 4th, etc. The second one: 1st and 2nd primes, then 3rd and 4th, then 5th and 6th, etc.
Bubba73You talkin' to me?18:24, 27 February 2018 (UTC)reply
Welcome to the Wikipedia Mathematics Reference Desk Archives
The page you are currently viewing is an archive page. While you can leave answers for any questions shown below, please ask new questions on one of the
current reference desk pages.
The first sum (let's denote it ) can be calculated in the following way:
.
On the other hand:
from where it is clear that
.
The value of can be calculated using the following integral
,
where the closed contour is chosen to go from to below the real axis and back above it. The only poles of the function under the integral are those of cotangent. Therefore . The final result is .
The second sum can be calculated in a similar way.
No, consecutive primes. The first one: 1st and 2nd primes, then 2nd and 3rd, then 3rd and 4th, etc. The second one: 1st and 2nd primes, then 3rd and 4th, then 5th and 6th, etc.
Bubba73You talkin' to me?18:24, 27 February 2018 (UTC)reply