Let `1, a_1, a_2, a_3, a_4` are `5^(th)` root of unity. If `sum_(i-1)^4 1/(2-a_2)=p/q` where `p and q` are in their lowest form. Find the value of `((p-q)/2)`

Let A={a_1,a_2,a_3,.....} and B={b_1,b_2,b_3,.....} are arithmetic sequences such that a_1=b_1!=0, a_2=2b_2 and sum_(i=1)^10 a_i=sum_(i=1)^15 b_j , If (a_2-a_1)/(b_2-b_1)=p/q where p and q are coprime then find the value of (p+q).

If a_1,a_2 ...a_n are nth roots of unity then 1/(1-a_1) +1/(1-a_2)+1/(1-a_3)..+1/(1-a_n) is equal to

If a_1,a_2,a_3,a_4 are in HP , then 1/(a_1a_4)sum_(r=1)^3a_r a_(r+1) is root of :

If 1, a_1,a_2,a_3 ,…, a_(n-1) are the nth roots of unity then prove that : (1-a_1)(1-a_2)(1-a_3)...(1-a_(n-1)) =n.

a_1,a_2,a_3 ,…., a_n from an A.P. Then the sum sum_(i=1)^10 (a_i a_(i+1)a_(i+2))/(a_i + a_(i+2)) where a_1=1 and a_2=2 is :

Let a_1, a_2 , a_3 and a_4 be in AP. If a_1 + a_4 =10 and a_2. a_3 =24 , then the least term of the AP, is

Let A be the set of 4-digit numbers a_1 a_2 a_3 a_4 where a_1 > a_2 > a_3 > a_4 , then n(A) is equal to

Let A be the set of 4-digit numbers a_1 a_2 a_3 a_4 where a_1 > a_2 > a_3 > a_4 , then n(A) is equal to