Find the sum of the infinite geometric series `1+3x+9x^2+27x^3+…..`

Find the sum of the infinite geometric series (1+1/3+1/9+1/27+...oo) .

Find the sum of the infinite geometric series (1-1/3+1/3^(2)-1/3^(3)+...oo) .

Find the sum of an infinite geometric series whose first term is the limit of the function f(x)=(tan x-sin x)/(sin^(3)x) as x rarr0 and whose common ratio is the limit of the function g(x)=(1-sqrt(x))/((cos^(-1)x)^(2)) as x->1

Find the sum of an infinite geometric series whose first term is the limit of the function f( x) =( tan x - sinx )/( sin^(3) x ) as x rarr 0 and whose common ratio is the limit of the function g(x) = ( 1-sqrt(x))/( (cos^(-1)x ) as x rarr 1

Find the sum of an infinite geometric series whose first term is lim_(x rarr0)sum_(k=1)^(2011)(((x)/(tan x)+2k))/(2011) and whose common ratio is the value of lim_(x rarr0)(e^(tan^(3)x)-e^(x^(3)))/(2ln(1+x^(3)sin^(2)x))[ Note: (y) denotes fractional part of yl.

Find the sum of the following geometric series: x^(3),x^(5),x^(7),rarr n terms

Find the sum of the infinite series 1^(2)+5^(2)x+9^(2)x^(2)+13^(2)x^(3)+...oo where |x|<1

Find the sum to ininity of the series 1-3x+5x^(2)+7x^(3)+....oo when lx|<1

Find the sum of the following geometric progression: 1,3,9,27, to 8 terms.

Find the sum of the following geometric series: (2)/(9)-(1)/(3)+(1)/(2)-(3)/(4)+rarr5 terms