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_(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.

A_1,A_2,..., A_n are the vertices of a regular plane polygon with n sides and O as its centre. Show that sum_(i=1)^n vec (OA)_i xx vec(OA)_(i+1)=(1-n)(vec (OA)_2 xx vec(OA)_1)

The difference between an exterior angle of (n-1) sided regular polygon and an exterior angle of (n+2) sided regular polygon is 6^(@) . Find the value of n

If a_1,a_2,a_3, ,a_n are an A.P. of non-zero terms, prove that 1/(a_1a_2)+1/(a_2a_3)++1/(a_(n-1)a_n)= (n-1)/(a_1a_n)

If A_1,A_2,....A_n are n independent events such that P(A_k)=1/(k+1),K=1,2,3,....,n; then the probability that none of the n events occur is

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

Let {a_n}(ngeq1) be a sequence such that a_1=1,a n d3a_(n+1)-3a_n=1fora l lngeq1. Then find the value of a_(2002.)

Let {a_n}(ngeq1) be a sequence such that a_1=1,a n d3a_(n+1)-3a_n=1 for all ngeq1. Then find the value of a_(2002.)

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

Let A_1,A_2,A_3,...,A_n are n Points in a plane whose coordinates are (x_1,y_1),(x_2,y_2),....,(x_n,y_n) respectively. A_1A_2 is bisected at the point P_1,P_1A_3 is divided in the ratio 1:2 at P_2,P_2A_4 is divided in the ratio 1:3 at P_3,P_3A_5 is divided in the ratio 1:4 at P_4 and the so on until all n points are exhausted. find the coordinates of the final point so obtained.