The sum to infinity of the series `1+2r+3r^2+4r^3`+…..is 9/4 , then value of r is

If the sum to infinity of the series 3+(3+d)1/4+(3+2d)1/(4^2)+oo is (44)/9 , then find ddot

In an infinite geometric series the first term is a and common ratio is r . If the sum of the series is 4 and the seond term is 3/4 , then (a, r) is

Let r_(1), r_(2) and r_(3) be the solutions of the equation x^(3) - 2 x^(2)+4 x+5074=0 , then the value of (r_(1) +2)(r_(2)+2)(r_(3)+2)

Let a+a r_1+a r1 2++ooa n da+a r_2+a r2 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_2dot Then the value of (r_1+r_2) is ________.

If S_p denotes the sum of the series 1+r^p+r^(2p)+ toooa n ds_p the sum of the series 1-r^(2p)r^(3p)+ tooo,|r|<1,t h e nS_p+s_p in term of S_(2p) is

The sum of the series 1/(2!) - 1/(3!) + 1/(4!) - …….. upto infinity is

If ""^(4)C_(r)=""^(4)C_(r+1) , then the value of r is

If the sum of the series Sigma_(n=0)^(oo) r^(n),|r|le 1 is s, then find the sum of the series Sigma_(n=0)^(oo) r^(2n),|r|le 1

Let for A=[(1,0,0),(2,1,0),(3,2,1)] , there be three row matrices R_(1), R_(2) and R_(3) , satifying the relations, R_(1)A=[(1,0,0)], R_(2)A=[(2,3,0)] and R_(3)A=[(2,3,1)] . If B is square matrix of order 3 with rows R_(1), R_(2) and R_(3) in order, then The value of det. (2A^(100) B^(3)-A^(99) B^(4)) is

If |r| gt 1, x = a + a/r + a/r^(2) + .......... infty , y = b - b/r + b/r^(2) - ......... infty and z = c + c/r^(2) + c/r^(4) + ...... infty , then the value of (xy)/z =