[" Let "A_(1),A_(2),......,A_(n)" be the vertices of an "n" -sided regular polygon such that,"],[qquad (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_(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.

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.

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.

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_(1), a_(2), a_(3) ,…., a_(n) are the terms of arithmatic progression then prove that (1)/(a_(1)a_(2)) + (1)/(a_(2)a_(3)) + (1)/(a_(3)a_(4)) + ….+ (1)/(a_(n-1) a_(n)) = (n-1)/(a_(1)a_(n))

If a_(1),a_(2),a_(3),,a_(n) are an A.P.of non-zero terms, prove that _(1)(1)/(a_(1)a_(2))+(1)/(a_(2)a_(3))++(1)/(a_(n-1)a_(n))=(n-1)/(a_(1)a_(n))