Question 71383
First we need to find the nth term of the series, or in other words the general formula. To go from 3 to 2, multiply by 2/3, and to go from 2 to 4/3 again you must multiply by 2/3. So the geometric ratio r is 2/3 and since the sequence starts at 3, the initial term a=3. So using the infinite sum formula we get
{{{S=a/(1-r)}}}Note: r<0 for an infinite sum to converge
{{{S=3/(1-2/3)}}}
{{{S=3/1/3}}}
{{{S=9}}}
So as the sum of the infinite series is 9.