Question

 

 

gia

giải giúp mình với bài 3,5 nha ! thank you mn

Answer 1

Bài 1:

Ta có: \(S=\dfrac{1}{5\cdot9}+\dfrac{1}{9\cdot13}+\dfrac{1}{13\cdot17}+...+\dfrac{1}{41\cdot45}\)

\(=\dfrac{1}{4}\left(\dfrac{4}{5\cdot9}+\dfrac{4}{9\cdot13}+\dfrac{4}{13\cdot17}+...+\dfrac{4}{41\cdot45}\right)\)

\(=\dfrac{1}{4}\left(\dfrac{1}{5}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{13}+\dfrac{1}{13}-\dfrac{1}{17}+...+\dfrac{1}{41}-\dfrac{1}{45}\right)\)

\(=\dfrac{1}{4}\left(\dfrac{1}{5}-\dfrac{1}{45}\right)\)

\(=\dfrac{1}{4}\cdot\dfrac{8}{45}=\dfrac{2}{45}\)