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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
Ta có:
\(B=\left(1-\frac{1}{2}\right).\left(1-\frac{1}{3}\right).\left(1-\frac{1}{4}\right)........\left(1-\frac{1}{2017}\right).\left(1-\frac{1}{2018}\right)\)
\(\Rightarrow B=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}.......\frac{2016}{2017}.\frac{2017}{2018}\)
Đởn giản hết sẽ còn là:
\(\Rightarrow B=\frac{1}{2018}\)
1/3xD=1/(2x4)+1/(4x6)+...+1/(98x100)
2/3xD=2/(2x4)+2/(4x6)+...+1/(98x100)
2/3xD= 1/2-1/4+1/4-1/6+...+1/98-1/100
2/3xD=1/2-1/100
2/3xD=49/100
D=147/200
a,=25/6;7/6=25/6x6/7=25/7
b,=7/2x32/6=56/3
c,=17/5-11/10=34/10-11/10=23/10
d,=8/3+11/4=32/12+33/12=65/12
S=1/(1+2)+1/(1+2+3)+1/(1+2+3+4)+...+1/(1+2+3+4+...+10)
S=1/(2*3/2)+1/(3*4/2)+1/(4*5/2)+...+1/(10*11/2)
S=2(1/(2*3)+1/(3*4)+1/(4*5)+1/(5*6)+...+1/(10*11)
S=2(1/2-1/3+1/3-1/4+1/4-1/5+...+1/10-1/11)
S=2(1/2-1/11)
S=2*9/22
S=9/11
nho k cho minh voi nha
\(1\frac{1}{5};1\frac{1}{2};1\frac{3}{5};2\frac{1}{2};2\frac{2}{3}\)
\(\frac{1}{1+2}+\frac{1}{1+2+3}+\frac{1}{1+2+3+4}+\frac{1}{1+2+3+4+5}\)
\(=\frac{1}{1+2}\times\left(1+\frac{1}{1+2+3}\div\frac{1}{1+2}+\frac{1}{1+2+3+4}\div\frac{1}{1+2}+\frac{1}{1+2+3+4+5}\div\frac{1}{1+2}\right)\)
\(=\frac{1}{1+2}\times\left(1+\frac{1}{2}+\frac{3}{10}+\frac{1}{5}\right)\)
\(=\frac{1}{1+2}\times2\)
\(=\frac{2}{3}\)
=\(\frac{2}{3}\)