The sum of an infinite GP with first term `a` and common ratio `r` `(-1ltrlt1` `i.e. ,` `|r|lt1)` is `S=a/(1-r)`

The sum of an infinite GP is 18. If the first term is 6, the common ratio is

Assertion: x,y,z are in A.P., Reason: sum of an infinite G.P. having first term a and common ratio r is a/(1-r) where -1ltrlt1 (A) Both A and R are true and R is the correct explanation of A (B) Both A and R are true R is not te correct explanation of A (C) A is true but R is false. (D) A is false but R is true.

Write three terms of the GP when the first term : a 'and the common ratio r are given a=4, r=3

Prove that the sum of n terms of GP with first term a and common ratio r is given by S_(n)=a(r^(n)-1)/(r-1)

Prove that the nth term of the GP with first term a and common ratio r is given by a_(n)=ar^(n-1)

Let S_(k) , be the sum of an infinite geometric series whose first term is kand common ratio is (k)/(k+1)(kgt0) . Then the value of sum_(k=1)^(oo)(-1)^(k)/(S_(k)) is equal to

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 ?

Let S_n denote the sum of first n terms of a G.P. whose first term and common ratio are a and r respectively. On the basis of above information answer the following question: The sum of product of first n terms of the G.P. taken two at a time in (A) (r+1)/r S_nS_(n-1) (B) r/(r+1)S_n^2 (C) r/(r+1)S_nS_(n-1) (D) none of these