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Summation series 

https://snag.gy/3A9Ct4.jpg

please help with these two questions as they seem impossible

 Oct 7, 2018
 #1
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+1

Sorry, I can't see that the sum of Sigma is a multiple of 2017, which is a prime number !! Even though they ask to prove it without summing it up, I still summed it up and got 1,986,985,000 which is no multiple of 2017. In order for the sum to be a multiple of 2017, it has to sum up to 1,986,985,023 !!!.

 Oct 7, 2018
 #3
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Yes, it sums up to what Rom got! Your mistake was summing up 6r^2 - 32r. It is 6r^2 + 32r !!.

Guest Oct 8, 2018
 #2
avatar+6251 
+2

two formulas are of use

 

nr=1 r2=16n(n+1)(2n+1)nr=1 r=12n(n+1)applying these we get, after some algebranr=1 6r2+32r=n(n+1)(2n+17)plugging n=1000 into the rightmost factor we see that 2(1000)+17=2017and thus the overall sum is a multiple of 2017

 Oct 8, 2018

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