# Sequence

Algebra Level 4

$S=\dfrac{5}{1 \times 3 \times 7}+\dfrac{7}{3 \times 5 \times 9}+\dfrac{9}{5 \times 7 \times 11}+\cdots$

If $$45S = n^2+ 1$$, where $$n$$ is a positive integer, find $$n$$.

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