已知函数f(n)=log(n+1)(n+2)(n∈N*),定义使f(1),f(2)……f(K)为整数的数k(k∈N*)叫

1＜f(n)=log(n+1)(n+2)≤100
n+1＜(n+1)^f(n)=n+2≤(n+1)^100
n≥1
3＜2^f1≤n+2≤(n+1)^100,
f1≥2
4≤2^f1≤n+2≤(n+1)^100,
n≥2
4≤3^f2≤n+2≤(n+1)^100
f2≥2,
9≤3^f2≤n+2≤(n+1)^100
n≥7
9≤8^f7≤n+2≤(n+1)^100
f7≥2,
64≤8^f7≤n+2≤(n+1)^100
n≥62
64≤63^f62≤n+2≤(n+1)^100
f62≥2,
63^2≤63^f62≤n+2≤(n+1)^100
所以填0.

f(n)=log(n+1)(n+2)=[ln(n+2)]/[ln(n+1)]
a1*a2*a3*......*an
=(ln3/ln2)(ln4/ln3)(ln5/ln4)...[ln(n+1)/ln(n)][ln(n+2)/ln(n+1)]
=1/(ln2)*(ln3/ln3)(ln4/ln4)(ln5/ln5)
....[ln(n)]/[ln(n)]*[...