Definite Integral 2

Calculus Level 4

Evaluate

\[5050 \times \frac{\displaystyle \int_{0}^{1}(1-x^{50})^{100}dx}{\displaystyle \int_{0}^{1}(1-x^{50})^{101}dx}\]

This problem is a part of my set Some JEE problems

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