一題證明 1/a+1/b+1/c=1/a+b+c 證1/a^n+1/b^n+1/c^n=1/(a+b+c)^n

若\(\displaystyle \frac{1}{a}+\frac{1}{b}+\frac{1}{c}=\frac{1}{a+b+c}\)，試證明\(\displaystyle \frac{1}{a^n}+\frac{1}{b^n}+\frac{1}{c^n}=\frac{1}{(a+b+c)^n}\)