Find the sum to infinity of the series `2+1+(1)/(2)+...oo.`

Find the sum to infinity of the series: 1+(3)/(2)+(5)/(2^(2))+(7)/(2^(3))+.........oo

Find the sum to infinity of the series 1 + (1+a)r+(1 + a + a ^(2))r^(2) + … where 0 lt a, r le 1

Find the sum to infinity of the series 1 + (1+a)r+(1 + a + a ^(2))r^(2) + … where 0 lt a, r le 1

Find the sum to infinity of the series 1^(2)+2^(2)x+3^(2)x^(2)+oo

Find the sum to infinity of the series 1-3x+ 5x^(2)+7x^(3)+ cdots oo when |x| lt 1 .

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

In the sum to infinity of the series 3+(3+x) (1)/(4) + (3+2x)(1)/(4^(2))+ ..... "is" (44)/(9) find x.

If p is positive, then the sum to infinity of the series, 1/(1+p) -(1-p)/(1+p)^2 + (1-p)^2/ (1+p)^3 -........ is

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