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 G.P. whose common ratio is numerically less than 1 is 32 and the sum of the first two terms is 24. Find the terms of G.P.

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.

The first term of an infinite G.P. is 1 any term is equal to the sum of all the succeeding terms. Find the series.

Find the common ratio of an infinte GP. Whose each term is ten times the sum of all its succeding terms.

If the first term of an infinite G.P. is 1 and each term is twice the sum of the succeeding terms, then the sum of the series is

If there be n quantities in G.P., whose common ratio is r and S_(m) denotes the sum of the first m terms, then the sum of their products, taken two by two, is

Find an infinite G.P. whose first term is 1 and each term is the sum of all the terms which follow it.

Sum of an infinite G.P. is 5/4 times the sum of all the odd terms. The common ratio of the G.P. is

The fifth term of a G.P. is 32 and common ratio is 2 , then the sum of first 14 terms of the G.P. is

If the sum of first two terms of an infinite G.P is 1 and every term is twice the sum of all the successive terms then its first term is