Re: [問題] 兩題數甲證明題
: 第一題用完二項式定理後就卡住了，
: 不太懂要怎麼把結果換成根好n分之2。
: 至於第二題貌似需要第一題的結果......
prove:n^(1/n) < 1 + sqrt(2/n)
n < (1+sqrt(2/n))^n = 1 + n*sqrt(2/n) + n(n-1)(2/n) + ... + (2/n)^(n/2)
^^^^^^^^^^^^^^^^^^^
= t
= 1 + sqrt(2n) + (2n-2) + t
= 2n + sqrt(2n) - 1 + t
since n belongs in Z+, sqrt(2n) > 1 and t > 0, so n < 2n + sqrt(2n) - 1 + t
then we can get n^(1/n) < 1 + sqrt(2/n).
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※ 編輯: j0958322080 (61.58.170.169), 09/19/2017 13:58:48
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