> 数学 >
已知正整数a.b满足
4
13
a
b
7
22
,则当b最小时,a+b的值为______.
人气:371 ℃ 时间:2020-02-03 02:22:00
解答
4
13
=
4
3×4+1
7
22
=
7
3×7+1

又∵
n
3n+1
=
1
3
-
1
9n+3

∴当n=5,即
n
3n+1
=
5
16
时,
4
13
5
16
7
22
,此时a+b=21,
当n=6时,即
n
3n+1
=
6
19
时,
4
13
6
19
7
22
,此时a+b=25,
∴当b最小时,a+b=21,
故答案为21.
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