已知an = log (n+1) (n+2),我们把使乘积a1a2…an为整数的数n称为“劣数”,则在区间(0,2005
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已知an = log (n+1) (n+2),我们把使乘积a1a2…an为整数的数n称为“劣数”,则在区间(0,2005)内所有劣数的个数为?
A.1024 B.2003 C.2026 D.2048
A.1024 B.2003 C.2026 D.2048
选 C.2026
你说的是以(n+1)为底吧
an=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)]*[ln(n+1)]/[ln(n+1)]*ln(n+2)
=[ln(n+2)]/ln2
=log(2)(n+2)
=k(k是整数)
得n+2=2^k
n=2^k-2
n
你说的是以(n+1)为底吧
an=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)]*[ln(n+1)]/[ln(n+1)]*ln(n+2)
=[ln(n+2)]/ln2
=log(2)(n+2)
=k(k是整数)
得n+2=2^k
n=2^k-2
n
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