Let `A_1,A_2,....A_n` be the vertices of an n-sided regular polygon such that ,`1/(A_1A_2)=1/(A_1A_3)+1/(A_1A_4)`. Find the value of n.

Let A_(1),A_(2),...A_(n) be the vertices of an n-sided regular polygon such that,(1)/(A_(1)A_(2))=(1)/(A_(1)A_(3))+(1)/(A_(1)A_(4)). Find the value of n.

Let A_(1), A_(2), A_(3),…,A_(n) be the vertices of an n-sided regular polygon such that (1)/(A_(1)A_(2))=(1)/(A_(1)A_(3))+(1)/(A_(1)A_(4)). Find the value of n. Prove or disprove the converse of this result.

If A_1A_2....A_n is a regular polygon. Then the vector vec(A_1A_2)+vec(A_2A_3)+.....vec(A_nA_1) is

let A_(1),A_(2),A_(3),...A_(n) are the vertices of a regular n sided polygon inscribed in a circle of radius R.If (A_(1)A_(2))^(2)+(A_(1)A_(3))^(2)+...(A_(1)A_(n))^(2)=14R^(2) then find the number of sides in the polygon.

If A_1A_2..........A_n is a regular polygon. Then the vectors overline(A_1A_2) + overline(A_2A_3)+.......+overline(A_nA_1) is equal to (A) 0 (B) n(vec(A_1A_2)) (C) n(vec(OA_1))(O is centre) (D) (n-1)(vec(A_1A_2))

If a_1, a_2, a_3, .... a_4001 are terms of an A.P. such that 1/(a_1a_2)+1/(a_2a_3)+1/(a_3a_4)+......1/(a_4000a_4001)=10 and a_2+a_4000=50, then |a_1-a_4001| is equal to

Let a_1,a_2,a_3,.... are in GP. If a_n>a_m when n>m and a_1+a_n=66 while a_2*a_(n-1)=128 and sum_(i=1)^n a_i=126 , find the value of n .

If A_1, A_2, …, A_n are n independent events, such that P(A_i)=(1)/(i+1), i=1, 2,…, n , then the probability that none of A_1, A_2, …, A_n occur, is

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.