Let `Delta_(r)=|(r-1,n,6),((r-1)^(2),2n^(2),4n-2),((r-1)^(3),3n^(3),3n^(2)-3n)|` Show that `sum_((r=1)) ^(n) Delta_(r)` is constant.

sum_(r=1)^(n) r.r ! is equal to

If Delta_(k) = |(1,n,n),(2k,n^(2)+n+1,n^(2)+n),(2k-1,n^(2),n^(2)+n+1)|and sum_(k=1)^(n)Delta_(k)=56. then n equals a)4 b)6 c)8 d)None of these

If Delta_(r)=|(2^(r)-1,2.3^(r)-1,4.5^(r)-1),(alpha,beta,gamma),(2^(n)-1,3^(n)-1,5^(n)-1)| then find the value of Delta .

If sum_(r=1)^(n) T_(r) = n(2n^(2)+9n +13) then find sum_(r=1)^(n) sqrt(T_(r)) .

Find the sum sum _(r=1)^(n) (r )/((r+1)!)

Prove that ""^nC_r+^nC_(r-1)=^(n+1)C_r

lim_(n to infty)(1^(2)/(1-n^(3))+2^(2)/(1-n^(3))+…+n^(2)/(1-n^(3))) is equal to :

Find the value of sum_(r=1)^(n-1)"sin"^(2)(rpi)/(n)