Question

n为整数,化简根号n（n+1）（n+2）（n+3）+1.并利用结果求,根号2000 乘以2001乘以2002乘以2003

Answer 1

√[n(n + 1)(n + 2)(n + 3)+ 1]

= √[(n² + 3n)(n² + 3n + 2) + 1]

= √[(n² + 3n)² + 2(n² + 3n) + 1]

= √ (n² + 3n + 1)²

= n² + 3n + 1

所以 √(2000×2001×2002×2003 + 1)

= 2000² + 3×2000 + 1

= 4000000 + 6000 + 1

= 4006001