已知数列{an}(n∈N*)满足:an=logn+1(n+2)(n∈N*),定义使a1·a2·a3·……ak为整数的数k(k∈N*)叫做企盼则区间【1,2004】内所有企盼数的和M=——
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![已知数列{an}(n∈N*)满足:an=logn+1(n+2)(n∈N*),定义使a1·a2·a3·……ak为整数的数k(k∈N*)叫做企盼则区间【1,2004】内所有企盼数的和M=——](/uploads/image/z/4538029-13-9.jpg?t=%E5%B7%B2%E7%9F%A5%E6%95%B0%E5%88%97%7Ban%7D%28n%E2%88%88N%2A%29%E6%BB%A1%E8%B6%B3%3Aan%3Dlogn%2B1%28n%2B2%29%28n%E2%88%88N%2A%29%2C%E5%AE%9A%E4%B9%89%E4%BD%BFa1%C2%B7a2%C2%B7a3%C2%B7%E2%80%A6%E2%80%A6ak%E4%B8%BA%E6%95%B4%E6%95%B0%E7%9A%84%E6%95%B0k%28k%E2%88%88N%2A%29%E5%8F%AB%E5%81%9A%E4%BC%81%E7%9B%BC%E5%88%99%E5%8C%BA%E9%97%B4%E3%80%901%2C2004%E3%80%91%E5%86%85%E6%89%80%E6%9C%89%E4%BC%81%E7%9B%BC%E6%95%B0%E7%9A%84%E5%92%8CM%3D%E2%80%94%E2%80%94)
已知数列{an}(n∈N*)满足:an=logn+1(n+2)(n∈N*),定义使a1·a2·a3·……ak为整数的数k(k∈N*)叫做企盼则区间【1,2004】内所有企盼数的和M=——
已知数列{an}(n∈N*)满足:an=logn+1(n+2)(n∈N*),定义使a1·a2·a3·……ak为整数的数k(k∈N*)叫做企盼
则区间【1,2004】内所有企盼数的和M=——
已知数列{an}(n∈N*)满足:an=logn+1(n+2)(n∈N*),定义使a1·a2·a3·……ak为整数的数k(k∈N*)叫做企盼则区间【1,2004】内所有企盼数的和M=——
an=log(n+1)(n+2)=lg(n+2)/lg(n+1)
a1a2...ak=(lg3/lg2)(lg4/lg3)...[lg(k+2)/lg(k+1)]=lg(k+2)/lg2=log2 (k+2)
k+2=2^p
k=2^p -2
令1≤2^p -2≤2004
3≤2^p≤2006
2≤p≤10
M=(2²-2)+(2³-2)+...+(2^10 -2)
=(2²+2³+...+2^10) -2×9
=4×(2^9 -1)/(2-1) -18
=2026