For all `n in N, Sigma n`

For all n in N , n(n + 1) (n + 5) is a multiple of 8

Let N be the set of all natural numbers, Z be the set of all integers and sigma:N to Z defined by sigma (n) = {{:(n/2, "," "if n is even"),( - (n-1)/(2) , "," "if n is odd "):} then

Let N be the set of all natural numbers, Z be the set of all integers and sigma:N to Z defined by sigma (n) = {{:(n/2, "," "if n is even"),( - (n-1)/(2) , "," "if n is odd "):}

If Sigma n = 210 " then " Sigma n^(2) =…….

Let nge3 be an integer. For a permutaion sigma=(a_(1),a_(2),.....,a_(n)) of (1,2,.....,n) we let f_(sigma)(x)=a_(n)X^(n-1)+a_(n-1)X^(x-2)+....+a_(2)x+a_(1) . Let S_(sigma) be the sum of the roots of f_(sigma)(x)=0 and let S denote the sum over all permutations sigma of (1,2,.....,n) of the numbers S_(sigma) . Then-