\(=\frac{0}{1.2}+\frac{0}{2.3}+\frac{0}{3.4}+...+\frac{0}{2015.2016}\)

\(=0+0+0+...+0=0\)

\(S=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+.......+\frac{1}{2015.2016}\)

\(S=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+.......+\frac{1}{2015}-\frac{1}{2016}\)

\(S=\frac{1}{1}-\frac{1}{2016}=\frac{2015}{2016}\)

làm r sao cứ đăng hoài vậy?

a: \(D=\frac{10}{100}+\frac{10}{150}+\frac{10}{210}+\cdots+\frac{10}{1200}\)

\(=\frac{1}{10}+\frac{1}{15}+\frac{1}{21}+\cdots+\frac{1}{120}\)

\(=\frac{2}{20}+\frac{2}{30}+\cdots+\frac{2}{240}=2\left(\frac{1}{4\cdot5}+\frac{1}{5\cdot6}+\cdots+\frac{1}{15\cdot16}\right)\)

\(=2\left(\frac14-\frac15+\frac15-\frac16+\cdots+\frac{1}{15}-\frac{1}{16}\right)=2\left(\frac14-\frac{1}{16}\right)=2\cdot\frac{3}{16}=\frac38\)

b: \(E=1\cdot2+2\cdot3+\cdots+99\cdot100\)

\(=1\left(1+1\right)+2\left(2+1\right)+\cdots+99\left(99+1\right)\)

\(=\left(1^2+2^2+\cdots+99^2\right)+\left(1+2+\cdots+99\right)\)

\(=\frac{99\left(99+1\right)\left(2\cdot99+1\right)}{6}+\frac{99\left(99+1\right)}{2}=\frac{99\cdot100\cdot199}{6}+99\cdot\frac{100}{2}\)

\(=33\cdot50\cdot199+99\cdot50\)

\(=33\cdot50\cdot\left(199+3\right)=33\cdot50\cdot202=33\cdot101\cdot100=333300\)

c: \(F=1^2+2^2+\cdots+98^2\)

\(=\frac{98\left(98+1\right)\left(2\cdot98+1\right)}{6}=\frac{98\cdot99\cdot197}{6}=49\cdot33\cdot197=318549\)

\(\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+...+\frac{1}{2016\cdot2017}\)

\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{2016}-\frac{1}{2017}\)

\(=1-\frac{1}{2017}=\frac{2016}{2017}\)

S=2-1/1.2  .  3-2/2.3............2016-2015/2015.2016

  =1/1 - 1/2 + 1/2 - 1/3+........+1/2015 - 1/2016

  =1/1 - 1/2016

   =2015/2016

tuyển gái dâm

\(=\frac{2015}{2016}\)

2015/2016 nhé bạn.