Square Summation

Algebra Level 2

Evaluate: 32+1321+52+1521+72+1721++992+19921.\large\dfrac{3^2+1}{3^2-1}+\dfrac{5^2+1}{5^2-1}+\dfrac{7^2+1}{7^2-1}+\cdots+\dfrac{99^2+1}{99^2-1}.

Note that 3,5,7,,993,5,7,\ldots,99 follows an arithmetic progression.

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