That's fine.
For part b), I think you've misunderstood what's being asked.
They initially want the ratio
P2n:Pn in it's simplest form without putting in values for n,R,A. And show that this ratio is greater than 1/2
Then with r=6.5, do the bit last bit involving 3/5.
One item to note: In your working you ended up with a fraction with
R2n−1 in the denominator. Notice that this is the difference to two squares, and so can be factorised.