Question

Bài 2...: Chứng minh A >B, biết: 

A=2/5x7 + 5/7x12 + 7/12x19 + 9/19x28 + 11/28x39 + 1/30x40

B=1/20 + 1/44 + 1/77 + 1/119 + 1/170

   

Answer 1

Sửa đề: 39*40

\(A=\dfrac{1}{5}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{12}+...+\dfrac{1}{39}-\dfrac{1}{40}=\dfrac{1}{5}-\dfrac{1}{40}=\dfrac{7}{40}\)

\(B=\dfrac{2}{3}\left(\dfrac{1}{5\cdot8}+\dfrac{1}{8\cdot11}+...+\dfrac{1}{17\cdot20}\right)\)

\(=\dfrac{2}{3}\left(\dfrac{1}{5}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{11}+...+\dfrac{1}{17}-\dfrac{1}{20}\right)\)

=2/3*3/20=2/20=1/10=4/40<A