Show that in an infinite G.P. with common ratio `r(|r|<1)` , each term bears a constant ratio to the sum of all terms that follow it.

Prove that in an infinite G.P. whose common ratio r is numerically less than one, the ratio of any term to the sum of all the succeeding terms is (1-r)/r

Prove that in an infinite G.P. whose common ratio r is numerically less than one, the ratio of any term to the sum of all the succeeding terms is (1-r)/r

The sum of an infinite GP is x and the common ratio r is such that |r|lt1 . If the first term of the GP is 2, then which one of the following is correct ?

If the sides of triangle ABC are in G.P with common ratio r (r<1) , show that r<1/2(sqrt5+1)

If the sides of triangle ABC are in G.P.with common ratio r(r<1), show that r<(1)/(2)(sqrt(5)+1)

The sum of an infinite GP with first term a and common ratio r(-1

Statement 1: If an infinite G.P. has 2nd term x and its sum is 4, then x belongs to (-8,1)dot Statement 2: Sum of an infinite G.P. is finite if for its common ratio r ,0<|r|<1.