(1)/(1)-(1)/(3)+(1)/(9)-(1)/(27)+cdots<

Find the sum of the infinite series (1)/(9) + (1)/(18) +(1)/(30) +(1)/(45)+(1)/(63)+cdots.

Find the sum to infinity of the following G.P. (i) 1, (1)/(3) , (1)/(9) . (1)/(27),… (ii) 2 , (-2)/(3) , (2)/(9) , (-2)/(27),… .

What is the sum of the infinite series 1-(1)/(3)+(1)/(9)-(1)/(27)+… ?

Find the sum of each of the following infinite geometric series, if it exists : 1 + (1)/(3) + (1)/(9) + (1)/(27) +…oo

(1)/(3)-(1)/(2).(1)/(9)+(1)/(3).(1)/(27)-(1)/(4).(1)/(81)+….oo=

(1)/(3)-(1)/(2).(1)/(9)+(1)/(3).(1)/(27)-(1)/(4).(1)/(81)+….oo=

If (1)/(1^(2))+(1)/(2^(2))+(1)/(3^(2))+cdots "to" oo = (pi^(2))/(6) then (1)/(1^(2)) +(1)/(3^(2))+(1)/(5^(2))+cdots equals

(1)/(2) + (1)/(4) + (1)/(8) + (1)/(16) + ….. = x , (1)/(3) + (1)/(9) + (1)/(27) + (1)/(81) + … = y, then