How do you find the sum of the infinite geometric series 1/3+1/9+1/27+1/81+...?

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Answer 1 · 2015-12-09T06:48:57

#Soo= 1/2#

Formula for sum of infinite geometric series is
#S_oo=a_1/(1-r)# ; #" " " " " -1 < r < 1#

We have a geometric series :#1/3 + 1/9 + 1/81+.........#

First we know #a_1= 1/3# (the first term)

Second: Identify #r# , we know #r= a_2/a_1# or #r= a_n/a_(n-1#

#r= (1/(9))/(1/3)# #hArr 1/9 *3/1 = 1/3 #

#r= 1/3#

Substitute into the formula
#Soo= (1/3)/(1-1/3) #

#= (1/3) /(2/3) #

#=(1/3)*(3/2)#

#Soo= 1/2#