Question

Cho \(M=\frac{1}{2}+\frac{2}{3}+\frac{3}{4}+\frac{4}{5}+\frac{5}{6}+\frac{6}{7}+\frac{7}{8}+\frac{8}{9}+\frac{9}{10}\)

So sánh M với 1

Answer 1

Ta có:

1 = \(\frac{1}{10}+\frac{1}{10}+\frac{1}{10}+............+\frac{1}{10}\)(10 phân số \(\frac{1}{10}\))

Mà \(\frac{1}{2}>\frac{1}{10};\frac{2}{3}>\frac{1}{10};............;\frac{9}{10}>10\)

\(\Rightarrow M>1\)

Vậy M > 1

Answer 2

Ta có:

1/2=0,5

2/3>0,6

<=>1/2+2/3>1,1>1

<=>1/2+2/3+3/4+...+9/10>1

Answer 3

Vì 1 = \(\frac{1}{10}+\frac{1}{10}+...+\frac{1}{10}\)

\(\Rightarrow\)M > 1 vì \(\frac{1}{2}>\frac{1}{10};\frac{2}{3}>\frac{1}{10};...;\frac{9}{10}>\frac{1}{10}\)

\(\Rightarrow M>1\)

Answer 4

Ta có:\(\frac{1}{2}+\frac{2}{3}+\frac{3}{4}+....+\frac{9}{10}\)

\(=\left(\frac{1}{2}+\frac{2}{3}\right)+\left(\frac{3}{4}+\frac{4}{5}+....+\frac{9}{10}\right)\)

\(=\left(\frac{3}{6}+\frac{4}{6}\right)+\left(\frac{3}{4}+\frac{4}{5}+....+\frac{9}{10}\right)\)

\(=\frac{7}{6}+\left(\frac{3}{4}+\frac{4}{5}+....+\frac{9}{10}\right)>\frac{6}{6}=1\)

\(\Rightarrow\frac{1}{2}+\frac{2}{3}+\frac{3}{4}+....+\frac{9}{10}>1\)

Bn Siêu sao bóng đá sai rồi

M chỉ có 9 phân số thì nó chỉ lớn hơn \(\frac{9}{10}\)