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a, đề phải là 1/a.(a+1) = 1/a - 1/a+1 chứ bạn !
Có : 1/a.(a+1) = (a+1)-a/a.(a+1) = a+1/a.(a+1) - a/a.(a+1) = 1/a - 1/a+1
=> 1/a.(a+1) = 1/a - 1/a+1
b, Có : 2/a.(a+1).(a+2) = (a+2)-a/a.(a+1).(a+2) = a+2/a.(a+1).(a+2) - a/a.(a+1).(a+2) = 1/a.(a+1) - 1/(a+1).(a+2)
=> 2/a.(a+1).(a+2) = 1/a.(a+1) - 1/(a+1).(a+2)
Tk mk nha
a, \(VP=\frac{1}{a}-\frac{1}{a+1}=\frac{a+1}{a\left(a+1\right)}-\frac{a}{a\left(a+1\right)}==\frac{a+1-a}{a\left(a+1\right)}=\frac{1}{a\left(a+1\right)}=VT\)
b, \(VP=\frac{1}{a\left(a+1\right)}-\frac{1}{\left(a+1\right)\left(a+2\right)}=\frac{a+2}{a\left(a+1\right)\left(a+2\right)}-\frac{a}{a\left(a+1\right)\left(a+2\right)}=\frac{a+2-a}{a\left(a+1\right)\left(a+2\right)}=\frac{2}{a\left(a+1\right)\left(a+2\right)}=VT\)
a) \(\frac{1}{a\left(a+1\right)}=\frac{\left(a+1\right)-a}{a\left(a+1\right)}=\frac{a+1}{a\left(a+1\right)}-\frac{a}{a\left(a+1\right)}=\frac{1}{a}-\frac{1}{a+1}\)
b) \(\frac{2}{a\left(a+1\right)\left(a+2\right)}=\frac{\left(a+2\right)-a}{a\left(a+1\right)\left(a+2\right)}=\frac{a+2}{a\left(a+1\right)\left(a+2\right)}-\frac{a}{a\left(a+1\right)\left(a+2\right)}\)
\(=\frac{1}{a\left(a+1\right)}-\frac{1}{\left(a+1\right)\left(a+2\right)}\)
a, Ta có : \(\frac{1}{a}-\frac{1}{a+1}=\frac{a+1}{a\left(a+1\right)}-\frac{a}{a\left(a+1\right)}=\frac{a+1-a}{a\left(a+1\right)}\)
\(VT=\frac{1}{a\left(a+1\right)}\left(đpcm\right)\)
b, Ta có : \(\frac{1}{a\left(a+1\right)}-\frac{1}{\left(a+1\right)\left(a+2\right)}=\frac{a+2}{a\left(a+1\right)\left(a+2\right)}-\frac{a}{a\left(a+1\right)\left(a+2\right)}\)
\(VT=\frac{2}{a\left(a+1\right)\left(a+2\right)}\left(đpcm\right)\)
a) \(\frac{1}{a\left(a+1\right)}=\frac{a+1-a}{a\left(a+1\right)}=\frac{a+1}{a\left(a+1\right)}-\frac{a}{a\left(a+1\right)}=\frac{1}{a}-\frac{1}{a+1}\)
b)\(\frac{2}{a\left(a+1\right)\left(a+2\right)}=\frac{a+2-a}{a\left(a+1\right)\left(a+2\right)}=\frac{a+2}{a\left(a+1\right)\left(a+2\right)}-\frac{a}{a\left(a+1\right)\left(a+2\right)}=\frac{1}{a\left(a+1\right)}-\frac{1}{\left(a+1\right)\left(a+2\right)}\)