bgcfd

đường cong parabol

A=1/2*3/4*..*99/100

=>A<2/3*4/5*6/7*...*100/101

=>A^2<2/3*4/5*...*100/101*1/2*3/4*...*99/100

=>A^2<1/101<1/100

=>A<1/10

 \(A=\dfrac{1}{2}.\dfrac{3}{4}.\dfrac{5}{6}...\dfrac{99}{100}\)

\(A< \left(\dfrac{1}{2}.\dfrac{3}{4}.\dfrac{5}{6}...\dfrac{99}{100}\right).\left(\dfrac{2}{3}.\dfrac{4}{5}.\dfrac{6}{7}...\dfrac{98}{99}\right)\)

\(\Rightarrow A=\dfrac{1}{2}.\dfrac{2}{3}.\dfrac{3}{4}.\dfrac{4}{5}.\dfrac{5}{6}.\dfrac{6}{7}...\dfrac{98}{99}.\dfrac{99}{100}\)

\(\Leftrightarrow A=\dfrac{1.2.3.4.5.6...98.99}{2.3.4.5.6.7...99.100}\)

\(\Rightarrow A< \dfrac{1}{100}< \dfrac{1}{10}\)

Vậy \(A< \dfrac{1}{10}\)

đặt \(B=\frac{2}{3}.\frac{4}{5}.\frac{6}{7}...\frac{98}{99}.\frac{100}{100}\Leftrightarrow A

cho a =1/2.3/4.5/6.....99/100.Chứng minh rằng:1/15<a<1/10.

ta co a < 2/3.4/5.....100/101 
nhan hai ve cho a ta co 
a^2 <2/3.4/5...100/101.1/2.3/4.5/6...99/100 
a^2<1/101 <1/100 
a< can 1/100 a <1/10.

Cm tương tự ta dc a>1/15.

Bn cx có thể kham khảo bài làm khác là:https://diendan.hocmai.vn/threads/toan-6-cmr-a-1-10-va-a-1-15.223994/

sao lại nhỏ hơn

vì: Ta có a:1/2=3/4.5/6.7/8...99/100

=> a<3/4.5/6..99/100

Để chứng minh A<1/10 thì ta chứng minh A<2/3.4/5.6/7....100/101

Để chứng minh A>1/15 thì ta chứng minh A>1/2.2/3.4/5.98/99