\(N=\frac{-7}{10^{2005}}+\frac{-7}{10^{2006}}+\frac{-8}{10^{2006}}\)

\(M=\frac{-7}{10^{2005}}+\frac{-8}{10^{2005}}+\frac{-7}{10^{2006}}\)

Ta xét M và N, ta có: \(\frac{-7}{10^{2005}}+\frac{-7}{10^{2006}}\text{ chung}\)

Mà: \(\frac{-8}{10^{2006}}>\frac{-8}{10^{2005}}\Rightarrow M>N\)

\(M=\frac{10^7+5}{10^7-8}=\frac{10^7-8+13}{10^7-8}=1+\frac{13}{10^7-8}\)

\(N=\frac{10^8+6}{10^8-7}=\frac{10^8-7+13}{10^8-7}=1+\frac{13}{10^8-7}\)

Ta có \(10^8-7>10^7-8\) \(=>\frac{13}{10^8-7}< \frac{13}{10^7-8}\) \(=>M< N\)

Vậy M<N

n<m nha ban

chuc ban hoc gioi

tk cho minh nha

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

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

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

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

\(\Rightarrow M>1\)

bằng nhau

Xét N ta có :

N = \(\frac{-7}{10^{2005}}\)+ \(\frac{-15}{10^{2006}}\)

N = \(\frac{-7}{10^{2005}}\)+ \(\frac{-7}{10^{2006}}\)+\(\frac{-8}{10^{2006}}\)

Xét M ta có :

M = \(\frac{-15}{10^{2005}}\)+\(\frac{-7}{10^{2006}}\)

M = \(\frac{-8}{10^{2005}}\)+\(\frac{-7}{10^{2005}}\)+ \(\frac{-7}{10^{2006}}\)

Vì \(\frac{-8}{10^{2006}}\)< \(\frac{-8}{10^{2005}}\) => N < M

Khó V~

ta có:M-N=\(\dfrac{-15}{10^{2005}}-\dfrac{-7}{10^{2005}}+\dfrac{-7}{10^{2006}}-\dfrac{-15}{10^{2006}}\)

=\(\dfrac{-8}{10^{2015}}\)+\(\dfrac{8}{10^{2016}}\)=8(\(\dfrac{1}{10^{2006}}-\dfrac{1}{10^{2005}}\))

Ta có:10²⁰⁰⁶>10²⁰⁰⁵<=>\(\dfrac{1}{10^{2006}}< \dfrac{1}{10^{2005}}\)

<=>\(\dfrac{1}{10^{2006}}-\dfrac{1}{10^{2005}}< 0\)

=>M-N<0 hay N>M

Chào bạn, bạn hãy theo dõi câu trả lời của mình nhé! 

a) Ta có : 

\(2^{225}=\left(2^3\right)^{75}=8^{75}\)

\(3^{151}=3^{150}\cdot3=\left(3^2\right)^{75}\cdot3=9^{75}\cdot3\)

Mà \(9^{75}>8^{75}=>9^{75}\cdot3>8^{75}=>3^{151}>2^{225}\)

b) Nhân cả vế A lẫn vế B với 10²⁰⁰⁵, ta có : 

\(10^{2005}A=-7+\frac{-15}{10}=\frac{-70}{10}+\frac{-15}{10}=\frac{-85}{10}\)

\(10^{2005}B=-15+\frac{-7}{10}=\frac{-150}{10}+\frac{-7}{10}=\frac{-157}{10}\)

Mà \(\frac{-85}{10}>\frac{-157}{10}=>10^{2005}A>10^{2005}B\)

\(=>A>B\)

Chúc bạn học tốt!

ơn bn nhìu

a) Ta có : 2²²⁵  =  (2³)⁷⁵ = 8⁷⁵ 

                3¹⁵¹  > 3¹⁵⁰ = (3²)⁷⁵ = 9⁷⁵

     Vi 8⁷⁵ < 9⁷⁵ nen 2²²⁵ < 3¹⁵⁰ 

    Ma 3¹⁵⁰ < 3¹⁵¹ \(\Rightarrow\)2²²⁵ < 3¹⁵¹

    Vay 2²²⁵ < 3¹⁵¹

b)  ban tu lam nhe !