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

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^pk=2^p -2令1≤2^p -2≤20043≤2^p≤20062≤p≤10M=(2²-2)+(2³-2)+...+(2^10 -2)=(2
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