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

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

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 S_(p) denotes the sum of the series 1+r^(p)+r^(2p)+rarr oo and S_(2p) the sum of the series 1-r^(p)+r^(2p)-rarr oo, prove that S_(+)S_(2p)=2S_(2p)

If the sum of an infinite G.P. is (7)/(2) and sum of the squares of its terms is (147)/(16) then the sum of the cubes of its terms is

In a G.P.the product of the first four terms is 4 and the second term is the reciprocal of the fourth term.The sum of infinite terms of the G.P is

The sum (S_(oo)) of infinite terms of A.G.P, (r<1) then S_(oo) is

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

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

If S_(p) denotes the sum of the series 1+r^(p)+r^(2p)+... to oo and s_(p) the sum of the series 1-r^(2p)r^(3p)+...*to oo,|r|<1, then S_(p)+s_(p) in term of S_(2p) is 2S_(2p) b.0 c.(1)/(2)S_(2p) d.-(1)/(2)S_(2p)