Q13/030) For any integer n=>1, prove that 1/6{n(n+1)(2n+1)} is an integer.?

that is n(n+1)(2n+1) is divisible by 6

n(n+1)(2n+1) = n(n+1)(n-1 + n + 2)
= n(n+1)(n-1) + n(n+1)(n+2)

1st number product of 3 consecutive numbers is divisible by 6 and 2nd number for the same reason

hence {n(n+1)(2n+1)} is divisible by 6 so 1/6{n(n+1)(2n+1)} is an integer.