If `U_(n)`=`|[1,K,K],[2n,K^(2)+K+1,K],[2n+1,K^(2)+K+1,K]|` and `sum_(n=1)^(K)U_(n)=-90` then absolute value of K is equal to

if U_n = |[1 , k , k] , [2n , k^2+k+1 , k^2+k] , [2n-1 , k^2 , k^2+k+1]| and sum_(k=1->n)U_n=72 then value of k is:

If sum_(k=0)^(n)(k^(2)+k+1)(k!)=(2018)(2018!) then the value of n is equal to

u_(n) = |{:(1,,k,,k),(2n,,k^(2)+k+1,,k^(2)+k),(2n-1,,k^(2),,k^(2)+k+1):}| and sum_(n=1)^(k) u_(n)=72 then k=

If sum_(n=1)^(5)(1)/(n(n+1)(n+2)(n+3))=(k)/(3), then k is equal to :-

If sum_(k=1)^(n)k=210, find the value of sum_(k=1)^(n)k^(2).

If D_k=|[1,n,n],[2k,n^2+n+2,n^2+n],[2k-1,n^2,n^2+n+2]| and sum_(k=1)^n D_k=48 ,then n equals (a)4 (b) 6 (c) 8 (d) none of these

If Delta_(k) = |(k,1,5),(k^(2),2n +1,2n +1),(k^(3),3n^(2),3n +1)|, " then " sum_(k=1)^(n) Delta_(k) is equal to

Let a_(n)=sum_(k=1)^(n)(1)/(k(n+1-k)), then for n>=2