If `a,ar,ar^(2),ar^(3),.......` are in G.P,then the sum of infinite terms of `GP,` if `|r|<1`=

If |r|<1, then the sum of infinite terms of G.P is

If s=a+ar+ar^(2)+ar^(3)+.......oo then s_(oo)= . (|r|<1)

In an infinite G.P. the sum of first three terms is 70. If the externme terms are multipled by 4 and the middle term is multiplied by 5, the resulting terms form an A.P. then the sum to infinite terms of G.P. is :

If the first term of the G.P is unity,and value of 4a_(2)+5a_(3) is minimum then find the sum to infinite terms

In G.P series a+ar+ar^(2)+ ----+oo Sum of infinite terms S_(oo) =

If each term of an infinite G.P.is twice the sum of the terms following it,then find the common ratio of the G.P.

Show that the products of the corresponding terms of the sequences a, ar,ar^(2),...,ar^(n-1) and A,AR,AR^(2),...,AR^(n-1) form a G.P,and find the common ratio.

Show that the products of the corresponding terms of the sequences a,ar,ar^(2),...,ar^(n-1) and a,AR,AR^(2),...,AR^(n-1) form a G.P,and find the common ratio.

a+ar_(1)+ar_(1)^(2)+...+oo and a+ar_(2)+ar_(2)^(2)+...+oo be two infinite series of positive numbers with the same first term.The sum of the first series is r_(1) and the sum of the second series r_(2). Then the value of (r_(1)+r_(2)) is