Question

Tính nhanh:

a) \(A=\dfrac{5}{1\cdot5}=\dfrac{5}{5\cdot10}+\dfrac{5}{10\cdot15}+...+\dfrac{5}{9995\cdot10000}\)

b) \(B=\dfrac{1}{420}+\dfrac{1}{462}+\dfrac{1}{506}+...+\dfrac{1}{1560}\)

Answer 1

a)\(A=\dfrac{5}{1\cdot5}+\dfrac{5}{5\cdot10}+\dfrac{5}{10\cdot15}+...+\dfrac{5}{9995\cdot10000}\)

\(=1-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{10}+...+\dfrac{1}{9995}-\dfrac{1}{10000}\)

\(=1-\dfrac{1}{10000}=\dfrac{9999}{10000}\)

b)\(B=\dfrac{1}{420}+\dfrac{1}{462}+\dfrac{1}{506}+...+\dfrac{1}{1560}\)

\(=\dfrac{1}{20\cdot21}+\dfrac{1}{21\cdot22}+\dfrac{1}{22\cdot23}+...+\dfrac{1}{39\cdot40}\)

\(=\dfrac{1}{20}-\dfrac{1}{21}+\dfrac{1}{21}-\dfrac{1}{22}+...+\dfrac{1}{39}-\dfrac{1}{40}\)

\(=\dfrac{1}{20}-\dfrac{1}{40}=\dfrac{1}{40}\)