正整数从1到n的连乘积叫做n的阶乘,.已知数列an的通项公式an=log(n+1)(2008!),则1/a1/+1/a2````+1/a2007=

题目

正整数从1到n的连乘积叫做n的阶乘,.已知数列an的通项公式an=log(n+1)(2008!),则1/a1/+1/a2````+1/a2007=

答案

an=log(n+1)(2008!)
1/an=log(2008!)(n+1)
1/a1+1/a2+...+1/a2007
=log(2008!)(1+1)+log(2008!)(2+1)+...+log(2008!)(2007+1)
=log(2008!)(2)+log(2008!)(3)+...+log(2008!)(2008)
=log(2008!)(2×3×...×2008)
=log(2008!)(1×2×3×...×2008)
=log(2008!)(2008!)
=1