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APMOPS 2011 Question 7

APMOPS · APMOPS 2011

Question 7

Find the value of $\frac{19}{20}+\frac{1919}{2020}+\frac{191919}{202020}+\cdots+\frac{\underbrace{1919\cdots19}_{2011\text{ copies of }19}}{\underbrace{2020\cdots20}_{2011\text{ copies of }20}}$.