" (i) "1+(1)/(3)+(1)/(9)+(1)/(27)+cdots oo

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

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.

Find the value of 9^((1)/(3)),9^((1)/(9)).9^((1)/(27))...up to oo

Prove that 9^((1)/(3)) xx 9^((1)/(9)) xx 9^((1)/(27))……oo = 3

Find the value of 9^(1/3), 9^(1/9). 9^(1/27)...up to oo.

Find the value of 9^(1/3). 9^(1/9). 9^(1/27)...up to 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

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