Question

Table
`IfDelta_(r)=|{:(,(2r), x, N(N+1)),(,(6r^(2)-1),y, N^(2)(2N+3)),(,(4r^(3) - 2Nr), z, N^(3)(N+1)):}|`
where N `in` natural numbers. Then `sum_(r=1)^(N) Delta_(r)` is
A. N
B. `N^(2)`
C. Zero
D. None of these

Answer 1

Correct Answer - 3
`underset(r=1)overset(N)sumDelta_(r)=|{:(,2N((N+1))/(2), x, N(N+1)),(,6N((N+1)(2N+1))/(6),y, N^(2)(2N+3)),(,4[(N(N+1))/(2)] -2N.(N(N+1))/(2), z, N^(3)(N+1)):}|=0`