\(\frac{T}{M}=\frac{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{100}}{\frac{1}{99}+\frac{2}{98}+...+\frac{98}{2}+\frac{99}{1}}\)

Xét M - 99 + 98 = \(\frac{100}{99}+\frac{100}{98}+...+\frac{100}{2}\)

\(\Leftrightarrow M-1=100\left(\frac{1}{2}+\frac{1}{3}+...+\frac{1}{99}\right)\)

\(\Rightarrow M=\frac{100}{100}+100\left(\frac{1}{2}+\frac{1}{3}+...+\frac{1}{99}\right)=100\left(\frac{1}{2}+\frac{1}{3}+...+\frac{1}{100}\right)\)

\(\Rightarrow\frac{T}{M}=\frac{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{100}}{100\left(\frac{1}{2}+\frac{1}{3}+...+\frac{1}{100}\right)}=\frac{1}{100}\)

\(M=\frac{99}{1}+\frac{98}{2}+\frac{97}{3}+...+\frac{2}{98}+\frac{1}{99}\)

cộng vào mỗi phân số trong 98 phân số sau,trừ phân số cuối đi 98 , ta được :

\(M=1+\left(\frac{98}{2}+1\right)+\left(\frac{97}{3}+1\right)+...+\left(\frac{2}{98}+1\right)+\left(\frac{1}{99}+1\right)\)

\(M=\frac{100}{100}+\frac{100}{2}+\frac{100}{3}+...+\frac{100}{98}+\frac{100}{99}\)

chuyển phân số \(\frac{100}{100}\)ra sau , ta được :

\(M=\frac{100}{2}+\frac{100}{3}+...+\frac{100}{98}+\frac{100}{99}+\frac{100}{100}\)

\(M=100.\left(\frac{1}{2}+\frac{1}{3}+...+\frac{1}{98}+\frac{1}{99}+\frac{1}{100}\right)\)

\(\Rightarrow\frac{M}{N}=\frac{100.\left(\frac{1}{2}+\frac{1}{3}+...+\frac{1}{98}+\frac{1}{99}+\frac{1}{100}\right)}{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{99}+\frac{1}{100}}=100\)

Thank bn na !!!

Ta có: \(\frac{99}{1}+\frac{98}{2}+\cdots+\frac{1}{99}\)

\(=\left(1+\frac{98}{2}\right)+\left(1+\frac{97}{3}\right)+\cdots+\left(1+\frac{1}{99}\right)+1\)

\(=\frac{100}{2}+\frac{100}{3}+\cdots+\frac{100}{99}+\frac{100}{100}\)

\(=100\left(\frac12+\frac13+\cdots+\frac{1}{100}\right)\)

Ta có: \(C=\frac{\frac12+\frac13+\frac14+\cdots+\frac{1}{100}}{\frac{99}{1}+\frac{98}{2}+\cdots+\frac{1}{99}}\)

\(=\frac{\frac12+\frac13+\cdots+\frac{1}{100}}{100\left(\frac12+\frac13+\cdots+\frac{1}{100}\right)}=\frac{1}{100}\)

M=1

N = 1-1/9 + 1-2/10 + 1-3/11 +...+ 1-92/100/1/45+1/50+1/55+...+1 /500

    = 8/9+8/10+8/11+8/12+...+8/100 / 1/5.9+1/5.10+1/5.11+...+1/ 5.100

    = 8 .(1/9+1/10+1/11+...+1/100) / 5 .(1/9+1/10+1/11+...+1/100)

     = 8/5

vậy tỉ số phần trăm của M và N là: 1:8/5= 62,5%

1-2+3-4+....+2015-2016+2017

=2017-2016+2015-2014+.....+4-3+2-1

=1+1+1+...+1(Có 1013 số 1)

= 1013

hmmmmmmmmmmmmmmmmmmmmmmm