Prove that: $$ q^{2} frac{left(1-q^(n-1} ight)left(1-q^(n-2) ight)}{(1-q)left(1- q^{2} ight)}+frac{left(1-q^(n-1) ight)}{(1-q)} $$ is a polynomial in $mathrm{q}$...

 

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Prove that: $$ q^{2} \frac{\left(1-q^(n-1} ight)\left(1-q^(n-2) ight)}{(1-q)\left(1- q^{2} ight)}+\frac{\left(1-q^(n-1) ight)}{(1-q)} $$ is a polynomial in $\mathrm{q}$ Prove that: $$ q^{2} \frac{\left(1-q^(n-1} ight)\left(1-q^(n-2) ight)}{(1-q)\left(1- q^{2} ight)}+\frac{\left(1-q^(n-1) ight)}{(1-q)} $$ is a polynomial in $\mathrm{q}$