Question

Cho M=\(\dfrac{9}{1}+\dfrac{8}{2}+\dfrac{7}{3}+...+\dfrac{1}{9}\)

N=\(\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}+...+\dfrac{1}{10}\)

Tình M:N

Answer 1

Ta có :

\(M=\dfrac{9}{1}+\dfrac{8}{2}+\dfrac{7}{3}+................+\dfrac{1}{9}\)

\(M=9+\dfrac{8}{2}+\dfrac{7}{3}+.........+\dfrac{1}{9}\)

\(M=\left(\dfrac{8}{2}+1\right)+\left(\dfrac{7}{3}+1\right)+.........+\left(\dfrac{1}{9}+1\right)+1\)

\(M=\dfrac{10}{2}+\dfrac{10}{3}+.............+\dfrac{10}{9}+\dfrac{10}{10}\)

\(M=10\left(\dfrac{1}{2}+\dfrac{1}{3}+...............+\dfrac{1}{10}\right)\)

Vậy \(\dfrac{M}{N}=\dfrac{10\left(\dfrac{1}{2}+\dfrac{1}{3}+...............+\dfrac{1}{10}\right)}{\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}+...............+\dfrac{1}{10}}=10\)