Question

[Kim Nam Khánh]

 

5	+	5	+ … +	5	=
9 x 11	11 x 13	143 x 145

Answer 1

[Nguyễn Lê Phước Thịnh]

\(\dfrac{5}{9\times11}+\dfrac{5}{11\times13}+...+\dfrac{5}{143\times145}\)

\(=\dfrac{5}{2}\left(\dfrac{2}{9\times11}+\dfrac{2}{11\times13}+...+\dfrac{2}{143\times145}\right)\)

\(=\dfrac{5}{2}\left(\dfrac{1}{9}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{13}+...+\dfrac{1}{143}-\dfrac{1}{145}\right)\)

\(=\dfrac{5}{2}\times\left(\dfrac{1}{9}-\dfrac{1}{145}\right)=\dfrac{5}{2}\times\dfrac{136}{1305}=\dfrac{68}{261}\)