Question

B= \(\dfrac{1}{4}\)+\(\dfrac{1}{12}\)+\(\dfrac{1}{24}\)+....+\(\dfrac{1}{79600}\)
C= \(\dfrac{2}{5}\)+\(\dfrac{2}{45}\)+\(\dfrac{2}{117}\)+....+\(\dfrac{2}{6885}\)
Trình bày đầy đủ cả phép tính nha
Tks:3

Answer 1

\(C=\dfrac{2}{5}+\dfrac{2}{45}+...+\dfrac{2}{6885}\)

\(=\dfrac{1}{2}\left(\dfrac{4}{1\cdot5}+\dfrac{4}{5\cdot9}+\dfrac{4}{9\cdot13}+...+\dfrac{4}{81\cdot85}\right)\)

\(=\dfrac{1}{2}\left(1-\dfrac{1}{85}\right)\)

\(=\dfrac{1}{2}\cdot\dfrac{84}{85}=\dfrac{42}{85}\)