\(B=\frac{1}{1x2x5}+\frac{1}{2x3x4}+\frac{1}{3x4x5}+...+\frac{1}{98x99x5}+\frac{1}{99x100x5}\)

\(5B=\frac{1}{1x2}+\frac{1}{2x3}+\frac{1}{3x4}+...+\frac{1}{98x99}+\frac{1}{99x100}\)

\(5B=\frac{2-1}{1x2}+\frac{3-2}{2x3}+\frac{4-3}{3x4}+...+\frac{99-98}{98x99}+\frac{100-99}{99x100}\)

\(5B=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{98}-\frac{1}{99}+\frac{1}{99}-\frac{1}{100}\)

\(5B=1-\frac{1}{100}=\frac{99}{100}\Rightarrow B=\frac{99}{500}\)

=1540/220

=7

ANH GIẢI NHƯ THẾ NÀO

Ta có: \(\frac{1}{1\times10}+\frac{1}{2\times9}+\cdots+\frac{1}{10\times1}\)

\(=2\times\left(\frac{1}{1\times10}+\frac{1}{2\times9}+\cdots+\frac{1}{5\times6}\right)\)

\(=\frac{2}{11}\times\left(\frac{11}{1\times10}+\frac{11}{2\times9}+\cdots+\frac{11}{5\times6}\right)\)

\(=\frac{2}{11}\times\left(1+\frac12+\frac13+\cdots+\frac19+\frac{1}{10}\right)\)

Ta có: \(A=\frac{1+\frac12+\cdots+\frac{1}{10}}{\frac{1}{1\times10}+\frac{1}{2\times9}+\cdots+\frac{1}{9\times2}+\frac{1}{10\times1}}\)

\(=\frac{1+\frac12+\cdots+\frac{1}{10}}{\frac{2}{11}\times\left(1+\frac12+\cdots+\frac{1}{10}\right)}=1:\frac{2}{11}=\frac{11}{2}\)

helpppppp meeeeeeee

Em nên gõ công thức trực quan để đề bài rõ ràng nhé

Ta có: \(1\times10+2\times9+\cdots+10\times1\)

\(=2\times\left(1\times10+2\times9+\cdots+5\times6\right)\)

\(=2\times\left(11+18+24+28+30\right)=2\times111=222\)

\(1+3+6+\cdots+45+55\)

\(=\frac{1\times2}{2}+\frac{2\times3}{2}+\frac{3\times4}{2}+\cdots+\frac{9\times10}{2}+\frac{10\times11}{2}\)

\(=\frac12\times\left(1\times2+2\times3+\cdots+10\times11\right)\)

\(=\frac12\times\left\lbrack1\times\left(1+1\right)+2\times\left(2+1\right)+\cdots+10\times\left(10+1\right)\right\rbrack\)

\(=\frac12\times\left\lbrack\left(1\times1+2\times2+\cdots+10\times10\right)+\left(1+2+\cdots+10\right)\right\rbrack\)

\(=\frac12\times\left\lbrack\frac{10\times\left(10+1\right)\times\left(2\times10+1\right)}{6}+\frac{10\times11}{2}\right\rbrack\)

\(=\frac12\times\left\lbrack\frac{10\times11\times21}{6}+5\times11\right\rbrack=\frac12\times\left\lbrack5\times11\times7+5\times11\right\rbrack\)

\(=\frac12\times55\times\left(7+1\right)=55\times\frac82=55\times4=220\)

Ta có: \(\frac{1+3+6+\cdots+45+55}{1\times10+2\times9+\cdots+10\times1}\)

\(=\frac{220}{222}=\frac{110}{111}\)