[math-fun] Infinite sum of a geometric sequence in a continuous fraction

Hello, with q in [0,1] v[i] and k[i] non-zero positive real numbers... n : 1/(v[0]+k[0]*q^2)=1/(v[0]+k[0]*(q^2*v[1]+q^5*k[1])/(v[1]+k[1]*(q^3*v[2]+q^7*k[2])/(v[2]+k[2]*(q^4*v[3]+q^9*k[3])/(v[3]+k[3]*(q^5*v[4]+q^11*k[4])/(v[4]+k[4]*(q^6*v[5]+q^13*k[5])/(v[5]+k[5]*(q^7*v[6]+q^15*k[6])/(v[6]+k[6]*(q^8*v[7]+q^17*k[7])/(v[7]+k[7]*(q^9*v[8]+q^19*k[8])/(v[8]+k[8]*(q^10*v[9]+q^21*k[9])/(v[9]+k[9]*(q^11*v[10]+q^23*k[10]     ))))))))))); When v[0]=k[0] 1/(v[0]+k[0]*q^2)=(1/k[0])*sum((-1)^n*q^2*n,n=0...infinite)