I see b) hasn't been done either. Using the ratio test:
An=(1/n){Pn/Qn}^2
An+1/An=[n/(n+1)]{(Pn+1/Qn+1)/(Pn/Qn)}^2
Pn=2*4*...*2n
Qn=1*3*...*(2n-1)
Pn+1=Pn*[2(n+1)]
Qn+1=Qn*[2(n+1)-1]=Qn*(2n+1)
after a little algebra
An+1/An=(4n^2+4n)/(4n^2+4n+1)<1 and sequence converges