Question

Bài 7: tính nhanh

3/1x3x5+3/3x5x7+3/5x7x9+...+3/37x39x41

                  cíu emmmmmmmmmmmm

 

Answer 1

\(\dfrac{3}{1\cdot3\cdot5}+\dfrac{3}{3\cdot5\cdot7}+\dfrac{3}{5\cdot7\cdot9}+\cdot\cdot\cdot+\dfrac{3}{37\cdot39\cdot41}\)

\(=\dfrac{3}{4}\left(\dfrac{4}{1\cdot3\cdot5}+\dfrac{4}{3\cdot5\cdot7}+\dfrac{4}{5\cdot7\cdot9}+\cdot\cdot\cdot+\dfrac{4}{37\cdot39\cdot41}\right)\)

\(=\dfrac{3}{4}\left(\dfrac{1}{1\cdot3}-\dfrac{1}{3\cdot5}+\dfrac{1}{3\cdot5}-\dfrac{1}{5\cdot7}+\dfrac{1}{5\cdot7}-\dfrac{1}{7\cdot9}+\cdot\cdot\cdot+\dfrac{1}{37\cdot39}-\dfrac{1}{39\cdot41}\right)\)

\(=\dfrac{3}{4}\left(\dfrac{1}{3}-\dfrac{1}{39\cdot41}\right)\)

\(=\dfrac{3}{4}\cdot\dfrac{532}{1599}=\dfrac{133}{533}\)

#Ayumu