Question

数列最大项问题

Answer 1

an从第16项开始变为正数，之前为负数，所以最大项至少在16项或之后

[n/(n-15.6)]-[(n+1)/(n+1-15.6)]

=[n(n+1-15.6)-(n+1)(n-15.6)]/[(n-15.6)(n+1-15.6)]

=15.6/[(n-15.6)(n+1-15.6)]

当n≥16时，上述式子小于0

也就是说an>a(n+1)

所以最大项即为第16项

Answer 2

a(n)/a(n-1)
=
9(n+1)/[10n]
=
[10n
+
9
-
n]/(10n)
=
1
+
(9-n)/(10n).
所以，n<9时，(9-n)/(10n)
>
0,
a(n)/a(n-1)
=
1
+
(9-n)/(10n)
>
1
n>9时，(9-n)/(10n)
<
0.
a(n)/a(n-1)
=
1
+
(9-n)/(10n)
<
1.