Sequence

Algebra Level 5

S=51×3×7+73×5×9+95×7×11+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=n2+145S = n^2+ 1, where nn is a positive integer, find nn.

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