Question

Bài tập tham khảo:
Bài 1: Tính tổng A = 1/3x5 + 1/5x7 + 1/7x9 + ......+1/37x39
 

Answer 1

\(A=\dfrac{1}{3.5}+\dfrac{1}{7.9}+...+\dfrac{1}{37.39}\\ =\dfrac{1}{2}\left(\dfrac{2}{3.5}+\dfrac{2}{7.9}+...+\dfrac{2}{37.39}\right)\\ =\dfrac{1}{2}\left(\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+...+\dfrac{1}{37}-\dfrac{1}{39}\right)\\ =\dfrac{1}{2}\left(\dfrac{1}{3}-\dfrac{1}{39}\right)\\ =\dfrac{1}{2}.\dfrac{4}{13}\\ =\dfrac{2}{13}\)

Answer 2

A=13.5+17.9+...+137.39=12(23.5+27.9+...+237.39)=12(13−15+15−17+...+137−139)=12(13−139)=12.413=213