really easy way to prove the first part take k = n , sum of the numbers will be n(n+1)/2 which is divisible by n when it is odd. thus there is no nice rearrangement
k(2k + 1) / 2k Cancel the common k term, which leaves: (2k + 1) / 2 Since 2k + 1 is odd and 2 is even, dividing an odd number by an even number does not yield an integer. Therefore, k(2k + 1) is never divisible by 2k.
really easy way to prove the first part
take k = n , sum of the numbers will be n(n+1)/2 which is divisible by n when it is odd.
thus there is no nice rearrangement
Really light problem
k(2k + 1) / 2k
Cancel the common k term, which leaves:
(2k + 1) / 2
Since 2k + 1 is odd and 2 is even, dividing an odd number by an even number does not yield an integer. Therefore, k(2k + 1) is never divisible by 2k.
k(2k+1) is never divisible by 2k because 2 doesn't divide 2k+1