Question

Bài 5: (0,75điểm)  Thực hiện phép tính \(\dfrac{2}{1.4}+\dfrac{2}{4.7}+...+\dfrac{2}{97.100}\)

Answer 1

\(\dfrac{2}{1\cdot4}+\dfrac{2}{4\cdot7}+...+\dfrac{2}{97\cdot100}\)

\(=\dfrac{2}{3}\left(1-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{7}+...+\dfrac{1}{97}-\dfrac{1}{100}\right)\)

\(=\dfrac{2}{3}\left(1-\dfrac{1}{100}\right)\)

\(=\dfrac{2}{3}\cdot\dfrac{99}{100}\)

\(=\dfrac{33}{50}\)

Answer 2

\(\dfrac{2}{1.4}+\dfrac{2}{4.7}+......+\dfrac{2}{97.100}\)

\(= \dfrac{2}{3} . ( \dfrac{3}{1.4}+\dfrac{3}{4.7}+......+\dfrac{3}{97.100})\)

\(= \dfrac{2}{3} . ( 1 - \dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{10}+.....+\dfrac{1}{97}-\dfrac{1}{100})\)

\(= \dfrac{2}{3} . ( 1 - \dfrac{1}{100})\)

\(= \dfrac{2}{3} . \dfrac{99}{100}\)

\(= \dfrac{66}{100}\)