Question

N=1/1×9+9/19×29+9/29×39+......+9/2019×2029 Giúp mình với mình đang cần gấp🥺🥺🥺

Answer 1

Sửa đề: \(\dfrac{1}{1.9}\rightarrow\dfrac{9}{9.19}\)

Giải:

\(N=\dfrac{9}{9.19}+\dfrac{9}{19.29}+\dfrac{9}{29.39}+...+\dfrac{9}{2019.2029}\) 

\(N=\dfrac{9}{10}.\left(\dfrac{10}{9.19}+\dfrac{10}{19.29}+\dfrac{10}{29.39}+...+\dfrac{10}{2019.2029}\right)\) 

\(N=\dfrac{9}{10}.\left(\dfrac{1}{9}-\dfrac{1}{19}+\dfrac{1}{19}-\dfrac{1}{29}+\dfrac{1}{29}-\dfrac{1}{39}+...+\dfrac{1}{2019}-\dfrac{1}{2029}\right)\) 

\(N=\dfrac{9}{10}.\left(\dfrac{1}{9}-\dfrac{1}{2029}\right)\) 

\(N=\dfrac{9}{10}.\dfrac{2020}{18261}\) 

\(N=\dfrac{202}{2029}\)