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 October 18th, 2016, 09:24 PM #2 Global Moderator   Joined: Dec 2006 Posts: 20,301 Thanks: 1971 After cancelling identical terms, your sum (for $n$ pairs of terms) is $\displaystyle \Delta2 - \Delta p_{n+1}$, where the $p_i$ are the primes. As $\Delta2 = 2$ and $\Delta p_{n+1}\to0$ as $n\to\infty$, your limit is exactly 2. Thanks from red
 October 18th, 2016, 11:03 PM #3 Newbie   Joined: Oct 2016 From: Mexico Posts: 2 Thanks: 0 wow, sounds pretty obvious when you explain it! thanks, I didn't see it that way... so I could just think of it as -3 and +3 cancelling out? same thing with the 5s and 7s and so on with every single prime, infinetly? Last edited by red; October 19th, 2016 at 12:01 AM.

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