`(1)/(2)+(3)/(4)+(9)/(8)+(27)/(16)+... oo`

(1)/(2) + (1)/(4) + (1)/(8) +(1)/(16) + …" to" oo is

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

Find the sum of the series 1-(3)/(2)+(5)/(4)-(7)/(8)+(9)/(16).........oo

1+(1)/(2). (3)/(5) + (1.3)/(2.4) . (9)/(25)+(1.3.5)/(2.4.6).(27)/(125)+…...oo=

Find the sum of each of the following infinite geometric series, if it exists : (1)/(3) - (2)/(9) + (4)/(27) - (8)/(81) +…oo

-(2)/(3)-(1)/(2)((4)/(9))-(1)/(3)((8)/(27))-(1)/(4)((16)/(81))-…..oo=

-(2)/(3)-(1)/(2)((4)/(9))-(1)/(3)((8)/(27))-(1)/(4)((16)/(81))-…..oo=

If 'omega' is a complex cube root of unity, then omega^(((1)/(3)+(2)/(9)+(4)/(27)+...oo))+omega^(((1)/(2)+(3)/(8)+(9)/(32)+...oo))=

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