Question

A=3/1.4+3/4.7+3/7.10+....+3/40.43+3/2015.2018

Tính giá trị của biểu thức

Answer 1

Giải:

\(A=\dfrac{3}{1.4}+\dfrac{3}{4.7}+\dfrac{3}{7.10}+...+\dfrac{3}{40.43}+\dfrac{3}{2015.2018}\)

\(\Leftrightarrow A=\dfrac{1}{1}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{10}+...+\dfrac{1}{40}-\dfrac{1}{43}+\dfrac{1}{2015}-\dfrac{1}{2018}\)

\(\Leftrightarrow A=\dfrac{1}{1}-\dfrac{1}{43}+\dfrac{1}{2015}-\dfrac{1}{2018}\)

\(\Leftrightarrow A=\dfrac{42}{43}+\dfrac{1}{2015}-\dfrac{1}{2018}\)

\(\Leftrightarrow A=0,977240464-\dfrac{1}{2018}\)

\(\Leftrightarrow A=0,9767449238\approx0,98\)

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