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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