\(A=\frac{1\cdot2+2\cdot4+3\cdot6+4\cdot8+5\cdot10}{3\cdot4+6\cdot8+9\cdot12+12\cdot16+15\cdot20}\)

\(=>A=\frac{1\cdot2+4\cdot1\cdot2+9\cdot1\cdot2+16\cdot1\cdot2+25\cdot1\cdot2}{3\cdot4+4\cdot3\cdot4+9\cdot3\cdot4+16\cdot3\cdot4+25\cdot3\cdot4}\)

\(=>A=\frac{\left(1+4+9+16+25\right)\cdot1\cdot2}{\left(1+4+9+16+25\right)\cdot3\cdot4}=\frac{1}{6}=\frac{111111}{666666}\)

Mà \(\frac{111111}{666666}< \frac{111111}{666665}\)

\(=>A< B\)

Ta có: \(K=\frac14+\frac19+\frac{1}{16}+\cdots+\frac{1}{10000}\)

=>\(K=\frac{1}{2^2}+\frac{1}{3^2}+\cdots+\frac{1}{100^2}\)

=>\(K<\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\cdots+\frac{1}{99\cdot100}\)

=>\(K<1-\frac12+\frac12-\frac13+\cdots+\frac{1}{99}-\frac{1}{100}\)

=>\(K<1-\frac{1}{100}\)

=>K<1

a) 5/16 > -9/24

b) 5/6>-1/2

c)-7/12<3/4

a, 5/16 > -9/24

 b, 5/6 > -1/2 

c, -7/12 < 3/4

a) \(\dfrac{3}{4}=\dfrac{3\times4}{4\times4}=\dfrac{12}{16}\)

b) \(\dfrac{1}{3}=\dfrac{1\times3}{3\times3}=\dfrac{3}{9}\)

c) \(\dfrac{5}{6}=\dfrac{5\times3}{6\times3}=\dfrac{15}{18}\)

rồi so sánh hai phân số mà bạn

A

A

\(7\dfrac{4}{5}và9\dfrac{1}{2}\\ Tacó:7< 9\\ \Rightarrow7\dfrac{4}{5}< 9\dfrac{1}{2}\\ 7\dfrac{1}{6}và3\dfrac{4}{5}\\ Tacó:7>3\\ \Rightarrow7\dfrac{1}{6}>3\dfrac{4}{5}\)

Câu cuối không phải hỗn số

A=1/(2x2)+1/(3x3)+...+1/(100x100) 
Nhận thấy rằng n x n -1=n x n -n+n-1=n x (n-1)+n-1=(n-1) x (n+1) 
=> A < 1/(2x2-1)+1/(3x3-1)+...+1/(100x100-1)=1/(1x3)+1/(3x5)+...+1/(99x101)=1/2-1/202<1/2<3/4