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

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Answer 1 · 2016-02-01T22:34:17

Use the formula for the sum of an infinite geometric series to find:

#1+1/3+1/9+... = 3/2#

The general term of a geometric series is given by the formula:

#a_n = a r^(n-1)#

where #a# is the initial term and #r# the common ratio.

The sum of an infinite geometric series is given by the formula:

#sum_(n=1)^oo a r^(n-1) = a/(1-r)#

when #abs(r) < 1#. Otherwise the series does not converge.

In our current example #a=1# and #r = 1/3#, so we find:

#sum_(n=1)^oo (1 * (1/3)^(n-1)) = 1/(1-1/3) = 1/(2/3) = 3/2#