求解这个不等式的详细过程 50
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10Cr . 2^(10-r) ≥ 10C(r-1) . 2^(10-r+1) (1)
10Cr . 2^(10-r) ≥ 10C(r+1) . 2^(10-r-1) (2)
r : 是1个非负整数 , 0≤r≤10 ;
from (1)
10Cr . 2^(10-r) ≥ 10C(r-1) . 2^(10-r+1)
10Cr/10C(r-1) ≥ 2
(r-1)! .(10-r+1)!/[ r! .(10-r)! ] ≥ 2
(10-r+1)/r ≥ 2
11-r ≥ 2r
r≤11/3 (3)
from (2)
10Cr . 2^(10-r) ≥ 10C(r+1) . 2^(10-r-1)
10C(r+1)/10Cr ≤ 2
(10-r)! . r! /[ (10-r-1)! . (r+1)! ] ≤ 2
(10-r)/(r+1) ≤ 2
10-r ≤ 2r +2
3r ≥ 12
r ≥ 4
10Cr . 2^(10-r) ≥ 10C(r+1) . 2^(10-r-1) (2)
r : 是1个非负整数 , 0≤r≤10 ;
from (1)
10Cr . 2^(10-r) ≥ 10C(r-1) . 2^(10-r+1)
10Cr/10C(r-1) ≥ 2
(r-1)! .(10-r+1)!/[ r! .(10-r)! ] ≥ 2
(10-r+1)/r ≥ 2
11-r ≥ 2r
r≤11/3 (3)
from (2)
10Cr . 2^(10-r) ≥ 10C(r+1) . 2^(10-r-1)
10C(r+1)/10Cr ≤ 2
(10-r)! . r! /[ (10-r-1)! . (r+1)! ] ≤ 2
(10-r)/(r+1) ≤ 2
10-r ≤ 2r +2
3r ≥ 12
r ≥ 4
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