Let `Delta_alpha=|[(alpha-1),n,6],[(alpha-1)^2,2n^2,4n-2],[(alpha-1)^3,3n^3,3n^2-3n]|`

Let Delta_(a)=|{:((a-1),n,6),((a-1)^(2), 2n^(2),4n-2),((a-1)^(3),3n^(3),3n^(2)-3n):}| the value of sum_(a=1)^(n)Delta_(a) is

Let Delta_(a)=|{:((a-1),n,6),((a-1)^(2), 2n^(2),4n-2),((a-1)^(3),3n^(3),3n^(2)-3n):}| the value of sum_(a=1)^(n)Delta_(a) is

Let Delta_(a)=|{:((a-1),n,6),((a-1)^(2), 2n^(2),4n-2),((a-1)^(3),3n^(3),3n^(2)-3n):}| the value of sum_(a=1)^(n)Delta_(a) is

The value of tan alpha+2tan(2 alpha)+4tan(4 alpha)+...+2^(n-1)tan(2^(n-1)alpha)+2^(n)cot(2^(n)alpha) is

If sum_(n=1)^nalpha_n=a n^2+b n ,w h e r ea ,b are constants and alpha_1,alpha_2,alpha_3 in {1,2,3,......,9}a n d25alpha_1,37alpha_2,49alpha_3 be three digit number, then prove that |[alpha_1,alpha_2,alpha_3],[ 5, 7, 9],[ 25alpha_1, 37alpha_2, 49alpha_3]|=0

If alpha_1, ,alpha_2, ,alpha_n are the roots of equation x^n+n a x-b=0, show that (alpha_(1)-alpha_(2))(alpha_(1)-alpha_(3))...(alpha_(1)-alpha_(n))=nalpha_(1)^(n-1)+nalpha

If alpha_1, ,alpha_2, ,alpha_n are the roots of equation x^n+n a x-b=0, show that (alpha_(1)-alpha_(2))(alpha_(1)-alpha_(3))...(alpha_(1)-alpha_(n))=nalpha_(1)^(n-1)+nalpha

If 1,alpha,alpha^2,alpha^3,…,alpha^(n-1) be the n^(th) roots of unity, then prove that 1^p+alpha^p+(alpha^2)^p+(alpha^3)^p+…+(alpha^(n-1))^p={{:(0,if" "pnekn),(n,if" "p=kn):}" where p,k"epsilonN