If `b_1, b_2 b_n` are the nth roots of unity, then prove that `^n C_1dotb_1+^n C_2dotb_2++^n C_ndotb_n-b/b{(1+b_2)^n-1}^dot`

If omega be a nth root of unity, then 1+omega+omega^2+…..+omega^(n-1) is (a)0(B) 1 (C) -1 (D) 2

If a>b and n is a positive integer,then prove that a^(n)-b^(n)>n(ab)^((n-1)/2)(a-b)

If tan B=(n sin A*cos A)/(1-n sin^(2)A), then prove that tan(A-B)=(1-n)tan A

A B C is a right-angled triangle in which /_B=90^0 and B C=adot If n points L_1, L_2, ,L_nonA B is divided in n+1 equal parts and L_1M_1, L_2M_2, ,L_n M_n are line segments parallel to B Ca n dM_1, M_2, ,M_n are on A C , then the sum of the lengths of L_1M_1, L_2M_2, ,L_n M_n is (a(n+1))/2 b. (a(n-1))/2 c. (a n)/2 d. none of these

If n. sin(A+2B)=sinA , then prove that: tan(A+B)=(1+n)/(1-n).tanB

If 1,alpha_1, alpha_2, …alpha_(n-1) be nth roots of unity then (1+alpha_1)(1+alpha_2)……....(1+alpha_(n-1))= (A) 0 or 1 according as n is even or odd (B) 0 or 1 according as n is odd or even (C) n (D) -n

If b_(1),b_(2),b_(3),"….."b_(n) are positive then the least value of (b_(1) + b_(2) +b _(3) + "….." + b_(n)) ((1)/(b_(1)) + (1)/(b_(2)) + "….." +(1)/(b_(n))) is

If omega is a complex nth root of unity,then sum_(r=1)^(n)(a+b)omega^(r-1) is equal to (n(n+1)a)/(2) b.(nb)/(1+n) c.(na)/(omega-1) d.none of these

If alpha is the nth root of unity,then 1+2 alpha+3 alpha^(2)+rarr n terms equal to a.(-n)/((1-alpha)^(2)) b.(-n)/(1-alpha^(2)) c.(-2n)/(1-alpha) d.(-2n)/((1-alpha)^(2))

If one root is nth power of the other root of this equation x^(2)-ax+b=0 then b^(n/(n+1))+b^(1/(n+1))=