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How do you find the sum of the infinite geometric series 2+2/3+2/9+2/27+...?

1 Answer

Jul 10, 2016

#3.#

Explanation:

Let #s# denote the reqd. sum. Then, we know that,

#s=a/(1-r)#, where, #a=# the first term of the series, and, #r,#common ratio, with #|r|<1#.

Here, #a=2#, and #r=#second term/first term#=(2/3)/2=1/3#, hence #|r|<1.#

Therefore, #s=2/(1-1/3)=2/(2/3)=3#

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