规定x@y=x*(x+1)*(x+2)*...*(x+y-1),如2@4=2*3*4*5.已知n+1/n@3=1/575,求自然数_数学解答

规定x@y=x*(x+1)*(x+2)*...*(x+y-1),如2@4=2*3*4*5.已知n+1/n@3=1/575,求自然数n.
还要用文字解释说明一下

人气：120 ℃　时间：2019-11-07 04:01:49

解答

n@3=n(n+1)(n+2)
n+1/n@3=1/575
n+1/[n(n+1)(n+2)]得
1/n(n+2)=1/575
n^2+2n-575=0
n=23