To find the sum of the given series, we can first simplify each term and then add them together.

The general term of the series is given by: 3/(2n-1) x (2n+1), where n represents the position of the term in the series.

Let's simplify the first few terms:

Term 1: n = 1
3/(2(1)-1) x (2(1)+1) = 3/1 x 3 = 9

Term 2: n = 2
3/(2(2)-1) x (2(2)+1) = 3/3 x 5 = 5

Term 3: n = 3
3/(2(3)-1) x (2(3)+1) = 3/5 x 7 = 21/5

Term 4: n = 4
3/(2(4)-1) x (2(4)+1) = 3/7 x 9 = 27/7

Term 5: n = 5
3/(2(5)-1) x (2(5)+1) = 3/9 x 11 = 33/9 = 11/3

Now, let's add up these simplified terms:

9 + 5 + 21/5 + 27/7 + 11/3

To add these fractions, we need to find a common denominator. The least common multiple of 5, 7, and 3 is 105.

Multiplying each fraction by the appropriate factor to get a denominator of 105:

(9 x 105)/1 + (5 x 105)/5 + (21 x 105)/(5 x 7) + (27 x 105)/(7 x 3) + (11 x 105)/(3 x 5)

945/1 + 525/5 + 315/7 + 945/7 + 385/1

Now, we can add these fractions together:

(945 + 525 + 315 + 945 + 385)/1

3215/1

Therefore, the sum of the given series is 3215.