Let P(n) be the statement that "2n≥2n+1"
For n=3, 23 = 8 ≥ 7 = 2(3)+1
i.e. P(3) is true.
asume P(k) is true ∃k∈Z, k≥3, i.e. 2k≥2k+1
For n=k+1, 2(k+1) = 2(2k) ≥ 2(2k+1) = 4k+2 = 2(k+1)+2k > 2(k+1)+1
i.e. P(k+1) is also true.
By M.I., P(n) is true ∀n∈Z, n≥3
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由 G@ry 於 星期一 十二月 03, 2007 11:44 pm
[問題]離散數學的證明題
由 訪客 於 星期一 十二月 03, 2007 6:07 pm
證明
2n+1小於等於2n
for all integer n大於等於3
2n+1小於等於2n
for all integer n大於等於3