# Sequences and series (8)

Algebra Level 4

The $$n^{th}$$ term of the sequence is given by $$t_{n}= \dfrac{n^5 +n^3}{n^4+n^2+1}$$ and if sum of its $$n$$ terms can be expressed as $$S_{n}=a_{n}^2 +a+ \dfrac{1}{b_{n}^2 +b}$$, where $$a_{n}$$ and $$b_{n}$$ are the $$n^{th}$$ terms of some arithmetic progression and $$a,b$$ are some constants. Then find the positive integral value of $$\dfrac{b_{n}}{a_{n}}$$.

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