bn vào /h7.net/hoi-dap/toan-6/so-sanh-a-3-10-1-3-9-1-va-b-3-9-1-3-8-1--faq205231.html

Trả lời:

A = \(\frac{3^{10}+1}{3^9+1}=\frac{3.3^9+1}{3.3^8+1}=\frac{3^9+1}{3^8+1}\)= B

_Học tốt bạn nha_

\(A=\frac{1+5+5^2+...+5^9}{1+5+5^2+...+5^8}=\frac{1+5\left(1 +5+5^2+...+5^8\right)}{1+5+5^2+...+5^8}=5+\frac{1}{1+5+5^2+...+5^8} \)

\(B=\frac{1+3+3^2+....+3^9}{1+3+3^2+....+3^8}=\frac{1+3\left(1+3+3^2+....+3^8\right)}{1+3+3^2+....+3^8}=3+\frac{1}{1+3+3^2+....+3^8}\)

\(=5+\frac{1}{1+3+3^2+....+3^8}-2\)  

Có: \(\frac{1}{1+5+5^2+...+5^8}>0\)              và      \(\frac{1}{1+3+3^2+....+3^8}-2< 0\)

\(\Rightarrow A>B\)

\(M=\frac{1}{1.2}+\frac{2}{1.2.3}+.....+\frac{9}{1.2.3.....10}\)

\(M=\frac{2-1}{1.2}+\frac{3-1}{1.2.3}+....+\frac{10-1}{1.2......10}\)

\(M=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{6}+....+\frac{10}{1.2.....10}-\frac{1}{1.2.....10}\)

\(M=1-\frac{1}{1.2.3......10}\)

\(M=1-\frac{1}{3628800}\)

Vì \(1=1\)mà \(\frac{1}{3628800}< 1\)nên \(1-\frac{1}{3628800}< 1\)

Vậy \(M< 1\)

-A =( 1- 1/2 )(1 -1/3).....(1 -1/10)

    = 1/2 . 2/3 ..... 9/10

    = 1/10

-A = 1/10 nên A = -1/10

Vì 1/10 < 1/9 nên -1/10 > -1/9

Vậy A > -1/9

\(A=\left(\frac{1}{2}-1\right).\left(\frac{1}{3}-1\right)...\left(\frac{1}{10}-1\right)=-\frac{1}{2}.-\frac{2}{3}...-\frac{9}{10}\)

\(=\frac{-\left(1.2...9\right)}{2.3...10}=\frac{-1}{10}\)

A<-1/9

mk nghĩ là A>B

mk giải cho câu A rồi tự suy mấy câu khác nhé!

ta có : A = 10^8 + 2/10^8 - 1

     => A = 10^8 - 1 + 3/10^8 - 1

     => A = 1+ 3/10^8 - 1

          B = 10^8/10^8 - 3

    =>  B = 10^8 - 3 + 3/10^8 - 3

    =>  B = 1+ 3/10^8 - 3

vì 3/10^8 - 1 < 3/10^8 - 3

=> 1 + 3/10^8 - 1 < 1 + 3/10^8 - 3

=> A < B

vậy A < B

cách này cô dạy mk đó