\(\left(1+\dfrac{1}{3}+\dfrac{1}{5}+...+\dfrac{1}{99}\right)-\left(\dfrac{1}{2}+\dfrac{1}{4}+...+\dfrac{1}{98}\right)\)
\(=\left(1+\dfrac{1}{2}+\dfrac{1}{3}+...+\dfrac{1}{49}+\dfrac{1}{50}+....+\dfrac{1}{98}+\dfrac{1}{99}\right)-2\left(\dfrac{1}{2}+\dfrac{1}{4}+...+\dfrac{1}{98}\right)\)
\(=\left(1+\dfrac{1}{2}+...+\dfrac{1}{49}+\dfrac{1}{50}+...+\dfrac{1}{98}+\dfrac{1}{99}\right)-\left(1+\dfrac{1}{2}+...+\dfrac{1}{49}\right)\)
\(=\dfrac{1}{50}+\dfrac{1}{51}+...+\dfrac{1}{99}\) (đpcm)
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