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how is this series 3+ 9/4 +27/16 +81/64... is converge to 12?

i represent the series as 3^(n+1)/4^n n starts from 0 to infinity, is this correct formula

2 answers

3*[1 + 3/4 + (3/4)^2 + ...(3/4)^n]
As n-> infnity, this becomes
3*[1/(1 - (3/4)] = 3*4 = 12
As n gets larger the sum goes to 0
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