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

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

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

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

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

\(\left(1+1+1+1+1+1+1+1+1+1\right)=10.10x10=100\)

1+1+1+1+1+1+1+1+1+10=19

Ta có: \(1+3+6+10+\cdots+45+55\)

\(=\frac12\times\left(2+6+12+20+\cdots+90+110\right)\)

\(=\frac12\times\left(1\times2+2\times3+\cdots+9\times10+10\times11\right)\)

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

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

\(=\frac12\times\left\lbrack10\times\left(10+1\right)\times\frac{\left(2\times10+1\right)}{6}+10\times\frac{11}{2}\right\rbrack\)

\(=\frac12\times\left\lbrack10\times11\times\frac{21}{6}+5\times11\right\rbrack=\frac12\times\left\lbrack5\times11\times7+5\times11\right\rbrack\)

\(=\frac12\times5\times11\times\left(7+1\right)=\frac{55}{2}\times8=55\times4=220\)

Ta có: \(1\times10+9\times2+\cdots+10\times1\)

\(=2\times\left(1\times10+2\times9+3\times8+4\times7+5\times6\right)\)

\(=2\times\left\lbrack1\times\left(11-1\right)+2\times\left(11-2\right)+3\times\left(11-3\right)+4\times\left(11-4\right)+5\times\left(11-5\right)\right\rbrack\)

\(=2\times\left\lbrack11\times\left(1+2+3+4+5\right)-\left(1\times1+2\times2+3\times3+4\times4+5\times5\right)\right\rbrack\)

\(=2\times\left\lbrack11\times15-\left(1+4+9+16+25\right)\right\rbrack\)

=2x(165-55)

=2x110

=220

Ta có: \(\frac{1\times10+9\times2+\cdots+10\times1}{1+3+6+10+\cdots+45+55}\)

\(=\frac{220}{220}\)

=1

1x10=10

k minh nhe ban! thank you

1*10=10

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

0,1 * 10 = 1

chuẩn đét

0,1 * 10 = 1

chuẩn đét