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\(\frac{1}{2}\times\frac{1}{2}+\frac{1}{2}\times\frac{1}{3}+...+\frac{1}{5}\times\frac{1}{6}\)
\(=\frac{1}{4}+\frac{1}{2\times3}+\frac{1}{3\times4}+\frac{1}{4\times5}+\frac{1}{5\times6}\)
\(=\frac{1}{4}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}\)
\(=\frac{1}{4}+\frac{1}{2}-\frac{1}{6}\)
\(=\frac{3+6-2}{12}=\frac{7}{12}\)
\(\frac{1}{2}\)* \(\frac{1}{2}\)+ \(\frac{1}{2}\)*\(\frac{1}{3}\)+ \(\frac{1}{3}\)* \(\frac{1}{4}\)+ \(\frac{1}{4}\)* \(\frac{1}{5}\)+ \(\frac{1}{5}\)* \(\frac{1}{6}\)
=\(\frac{1}{2}\)* \(\frac{1}{6}\)= \(\frac{1}{12}\)
( Những phân số khác nhau bạn loại đi nhé tại mình ko làm được bước đó trên này bạn thông cảm nhé ! )
b) \(\frac{1}{5}:\frac{1}{3}\cdot\frac{\frac{1}{3}}{\frac{1}{5}}+1996\)
\(=\frac{3}{5}\cdot\left(\frac{1}{3}:\frac{1}{5}\right)+1996\)
\(=\frac{3}{5}\cdot\frac{5}{3}+1996\)
\(=1+1996=1997\)
a) \(\frac{2}{3}:\frac{5}{7}\cdot\frac{5}{7}\cdot\frac{2}{3}+1934\)
\(=\frac{2\cdot7}{5\cdot3}\cdot\frac{5\cdot2}{7\cdot3}+1934\)
\(=\frac{2\cdot7\cdot5\cdot2}{5\cdot3\cdot7\cdot3}+1996=\frac{4}{9}+1996\)
\(\frac{3}{2}+\frac{3}{8}+\frac{3}{32}+\frac{3}{128}+\frac{3}{512}\)
=\(\frac{3}{1.2}+\frac{3}{2.4}+\frac{3}{4.8}+\frac{3}{8.16}+\frac{3}{16.32}\)
=\(\frac{3}{1}-\frac{3}{2}+\frac{3}{2}-\frac{3}{4}+\frac{3}{4}-\frac{3}{8}+\frac{3}{8}-\frac{3}{16}+\frac{3}{16}-\frac{3}{36}\)
=\(\frac{3}{1}-\frac{3}{36}\)=\(\frac{35}{12}\)
???????????????????????????????????????????????????????????????????????????^_^
Ta có:
G=\(3\frac{5}{7}+4\frac{3}{5}+1\frac{2}{7}\)\(+3\frac{1}{5}-\frac{4}{5}\)
=\(3+\frac{5}{7}+4+\frac{3}{5}+1+\frac{2}{7}+3+\frac{1}{5}-\frac{4}{5}\)
=\(\left(3+4+1+3\right)+\left(\frac{5}{7}+\frac{3}{5}+\frac{2}{7}+\frac{1}{5}-\frac{4}{5}\right)\)
=\(11+\left[\left(\frac{5}{7}+\frac{2}{7}\right)+\left(\frac{3}{5}+\frac{1}{5}-\frac{4}{5}\right)\right]\)
=\(11+\left[\frac{7}{7}+\frac{0}{5}\right]\)
=\(11+\left[1+0\right]\)
=\(11+1\)
=12
ĐÃ GIẢI CHI TIẾT RÙI NHÉ. **** NHA
mk làm lun nha
=22/5+51/9+11/4+3/5+1/3+1/4
=(22/5+3/5)+(11/4+1/4)+(51/9+1/3)
=5+3+6
=14
**** cho mk nha
Đặt phân thức trên là D
=> D=(1+1+1+1+...+1+2013/2+2012/3+...+2/2013+1/2014)/(1/2+1/3+1/4+...+1/2014)
=> D=(1+2013/2+1+2012/3+1+2011/4+...+1+2/2013+1+1/2014+1)/(1/2+1/3+1/4+1/5+...+1/2014)
=> D=(2015/2+2015/3+2015/4+...+2015/2013+2015/2014+1)/(1/2+1/3+1/4+...+1/2014)
=> D=[2015*(1/2+1/3+1/4+1/5+....+1/2014)]/(1/2+1/3+1/4+1/5+...+1/2014)
=> D=2015
\(A=5+\frac{5}{1+2}+\frac{5}{1+2+3}+...+\frac{5}{1+2+3+...+100}\)
A = \(5+\frac{5}{1+2}+\frac{5}{1+2+3}+...+\frac{5}{1+2+3+..+100}\)
\(=5x\left(1+\frac{1}{1+2}+\frac{1}{1+2+3}+...+\frac{1}{1+2+3+...+100}\right)\)
\(=5x\left(1+\frac{1}{3}+\frac{1}{6}+...+\frac{1}{5050}\right)\)
\(=2x5x\left(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+...+\frac{1}{10100}\right)\)
\(=10x\left(\frac{1}{1x2}+\frac{1}{2x3}+\frac{1}{3x4}+...+\frac{1}{100x101}\right)\)
\(=10x\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{100}-\frac{1}{101}\right)\)
\(=10x\left(1-\frac{1}{101}\right)\)
\(=10x\frac{100}{101}\)
\(=\frac{1000}{101}\)
\(4\frac{2}{5}+5\frac{6}{9}+2\frac{3}{4}+\frac{3}{5}+\frac{1}{3}+\frac{1}{4}\)
\(=4+\frac{2}{5}+5+\frac{6}{9}+2+\frac{3}{4}+\frac{3}{5}+\frac{1}{3}+\frac{1}{4}\)
\(=4+\frac{2}{5}+5+\frac{2}{3}+2+\frac{3}{4}+\frac{3}{5}+\frac{1}{3}+\frac{1}{4}\)
\(=\left(\frac{2}{5}+\frac{3}{5}\right)+\left(\frac{2}{3}+\frac{1}{3}\right)+\left(\frac{3}{4}+\frac{1}{4}\right)+\left(4+5+2\right)\)
\(=1+1+1+11\)
\(=14\)
=22/5+51/9+11/4+3/5+1/3+1/4
=(22/5+3/5)+(11/4+1/4)+(51/9+1/3)
=5+3+6
=14
\(\frac{1}{3}+\frac{1}{3}+\frac{1}{3}+\frac{1}{5}+\frac{1}{5}+\frac{1}{5}\)
\(=\frac{1}{3}\times3+\frac{1}{5}\times3\)
\(=1+\frac{3}{5}\)
\(=\frac{8}{5}.\)
1/3+1/3+1/3+1/5+1/5+1/5=1+3/5=5/5+3/5=8/5