Question

chứng minh rầng a/n(n+a) bằng 1/n-1/n+a (n,a thuộc Z)

 

Answer 1

Ta có:

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

Hay  \(\frac{a}{n\left(n+a\right)}=\frac{1}{n}-\frac{1}{n+a}\left(đpcm\right)\)

Answer 2

Ta có: \(\frac{1}{n}\).\(\frac{1}{n+1}\)=\(\frac{1}{n.n+1}\) 

       \(\frac{1}{n}\) -\(\frac{1}{n+1}\)=\(\frac{n+1}{n.\left(n+1\right)}\)-\(\frac{n}{n.\left(n+1\right)}\)

                    =\(\frac{n+1-n}{n.\left(n+1\right)}\)=\(\frac{1}{n.\left(n+1\right)}\)

Chọn mình nhé