n=1,1-1/3=2/3=2/(n+2);
n=2,(1-1/3)(1-1/4)=(2/3)(3/4)=6/12=1/2=2/4=2/(n+2);
:
假设当n=N为非零自然数时,等式成立,即(1-1/3)(1-1/4)...[1-1/(N+2)]=2/(N+2);
则当n=N+1,
(1-1/3)(1-1/4)...[1-1/(N+1+2)]=[1-1/(N+1+2)]*2/(N+2)=[(N+2)/(N+3)]*2/(N+2)=2/(N+3)=2/(n+2);
等式成立.证毕