\(\frac{M}{N}=\frac{\frac{1}{2007}+\frac{2}{2006}+......+\frac{2006}{2}+\frac{2007}{1}}{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+.......+\frac{1}{2006}+\frac{1}{2007}}\)

\(\frac{M}{N}=\frac{\frac{1}{2007}+1+\frac{2}{2006}+1+.......+\frac{2007}{1}+1+\frac{2008}{2008}-2008}{\frac{1}{2008}+\frac{1}{2007}+\frac{1}{2006}+.....+\frac{1}{2}}\)

\(\frac{M}{N}=\frac{\frac{2008}{2007}+\frac{2008}{2006}+....+\frac{2008}{1}+\frac{2008}{2008}-2008}{\frac{1}{2008}+........+\frac{1}{2}}\)

đến đây là ra rùi ha 

ê tớ chẳng hiểu gì cả

cậu làm tắt à

please cậu giúp tớ cả bài đi mà

khong biet

Ta có
\(M=1+\left(-2\right)+\left(-2\right)^2+...+\left(-2\right)^{2006}\)
\(M=\left(-2\right)^0+\left(-2\right)^1+\left(-2\right)^2+...+\left(-2\right)^{2006}\)
\(-2M=\left(-2\right)^1+\left(-2\right)^2+\left(-2\right)^3+...+\left(-2\right)^{2007}\)
\(3M=M-\left(-2M\right)=\left(-2\right)^0-\left(-2\right)^{2007}\)
\(\Rightarrow M=\frac{3M}{3}=\frac{1+2^{2007}}{3}\)

\(Q=\sqrt{1+2006^2+\left(\dfrac{2006}{2007}\right)^2}+\dfrac{2006}{2007}\)  

   =\(1+2006+\dfrac{2006}{2007}+\dfrac{2006}{2007}\)

   =\(2007+\dfrac{4012}{2007}\)

   =\(\dfrac{2007^2}{2007}+4012\)

   =\(\dfrac{4028049}{2007}+\dfrac{4012}{2007}\)

  =\(\dfrac{4032061}{2007}\)

\(Q=\sqrt{1+2006^2+\dfrac{2006^2}{2007^2}}+\dfrac{2006}{2007}\)

\(=1+2006+\dfrac{2006}{2007}+\dfrac{2006}{2007}\)

\(=\dfrac{4032061}{2007}\)

\(M:N=\frac{\frac{2008}{1}+\frac{2007}{2}+\frac{2006}{3}+...+\frac{2}{2007}+\frac{1}{2008}}{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+...+\frac{1}{2008}+\frac{1}{2009}}\)

Ta có tử số bằng: 2008+2007/2+2006/3+2005/4+…..+2/2007+1/2008 
(Phân tích 2008 thành 2008 con số 1 rồi đưa vào các nhóm) 
= (1 + 2007/2) + (1 + 2006/3) + (1 + 2005/4) +... + (1 + 2/2007) + ( 1 + 1/2008) + (1) 
= 2009/2 + 2009/3 + 2009//4 + ……. + 2009/2007 + 2009/2008 + 2009/2009 
= 2009 x (1/2 + 1/3 + 1/4 + ... + 1/2007 + 1/2008 + 1/2009) 
Mẫu số: 1/2 + 1/3 + 1/4 + ... + 1/2007 + 1/2008 + 1/2009 
\(\Rightarrow M:N=\frac{2009.\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+...+\frac{1}{2008}+\frac{1}{2009}\right)}{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+...+\frac{1}{2008}+\frac{1}{2009}}=2009\)

- Mình dùng cách lớp 8 để làm câu b được không :)?

- Tham khảo câu b:

https://olm.vn/hoi-dap/tim-kiem?q=+++++++++++A=2006%5E2005+1/2006%5E2006+1B=2006%5E2006+1/2006%5E2007+1so+s%C3%A1nh+A+v%C3%A0+B&id=520258

:< dễ lém á , mng giúp mìn ii 

bai toan nay minh ?

tinh2M

xong lấy 2M+M

cong cac cap so doi 

rồi tính kết quả thôi dễ mà !!!!!!!!!!!!!!!!!

Áp dung công thức a²+b²=(a+b)x(a-b)

M=2007²-2006²+2005²-2004²+...-2²+1²

^{M=(2007+2006)x(2007-2006)+(2005+2004)x(2005-2004)+...+(3+2)x(3-2)+1}

^{M=4013x1+4009x1+...+5x1+1}

M=4013+4009+...+5+1.                    Có (4013-1):4+1=1004(số)

M=(4013+1)x1004:2=2015028