Crazy Minimum

Algebra Level 5

22+42+62++(2n)212+32+52++(2n1)2<1.01 \large \dfrac{2^2+4^2+6^2+\cdots+(2 n)^2}{1^2+3^2+5^2+\cdots+(2 n-1)^2}<1.01

Find the minimum positive integer nn satisfying the inequality above.

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