Evaluating a Fraction Involving Alternating Series and Summations (Without a Calculator)

Evaluating a Fraction Involving Alternating Series and Summations (Without a Calculator)

IP 1

Without the use of calculator, evaluate \(\frac{1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+\frac{1}{5}-\frac{1}{6}+...+\frac{1}{2025}-\frac{1}{2026}}{\frac{1}{1+2027}+\frac{1}{2+2028}+...+\frac{1}{1013+3039}}\).

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Answer:\(2\).

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