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It is free to join and offers a vast range of training.Q: Finding a particular solution of a recurrence relation The recurrence relation I have is: $$T(n)=\frac{2}{1+T(n-1)}+T(n-1)\cdot T(n-2)$$ I have derived a homogeneous solution by : $A\cdot L(n) + B\cdot U(n) $ Here, $A=\frac{1}{(1+x)^2}=1+2x+2x^2+2x^3+2x^4+....$ $B=x^2$ $\therefore \therefore \frac{1}{L(n)}=A+B\cdot n+n \cdot A\cdot B+n^2 \cdot A\cdot B^2+n^3 \cdot A\cdot B^3+...$ $\therefore L(n)=1-2n+2n^2-2n^3+2n^4-....$ $U(n)=x^2 \cdot (1-2n+2n^2-2n^3+2n^4-....)$ But I am unable to derive a particular solution for it. 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