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[1,2005]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[1,2005]内所有企盼数的和M=](/uploads/image/z/3183753-57-3.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%EF%BC%9Aan%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%5B1%2C2005%5D%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)
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[1,2005]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
[1,2005]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[1,2005]内所有企盼数的和M=
an=logn+1(n+2)=log2(n+2)/log2(n+1)
a1·a2·a3·……ak=log2(n+2)
n+2必须是2的n次幂才可以取的整数
M=(4-2)+(8-2)+(16-2)+…………+(1024-2)
=2^2+2^3+…………+2^10-2*9
=2026