Question

chứng minh :

a)

\(\frac{1}{a\left(a+1\right)}=\frac{1}{a}+\frac{1}{a+1}\)

b) \(\frac{2}{a\left(a+1\right)\left(a+2\right)}=\frac{1}{a\left(a+1\right)}-\frac{1}{a+2}\)

Answer 1

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)\(\frac{2}{a\left(a+1\right)\left(a+2\right)}=\frac{a+2-a}{a\left(a+1\right)\left(a+2\right)}=\frac{a+2}{a\left(a+1\right)\left(a+2\right)}-\frac{a}{a\left(a+1\right)\left(a+2\right)}=\frac{1}{a\left(a+1\right)}-\frac{1}{\left(a+1\right)\left(a+2\right)}\)