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QUESTION

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

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