N n 2 n 2
You proved it's true for n=5. Now suppose it's true for some integer n≥5. The aim is to prove it's true for n+1. But (♤)2n+1=2×2n>2×n2>(n+1)2. ,n2<2n⟺2logn<nlog2⟺lognn<log22. But we know that lognn→n→∞0 , so the above inequality's definitely true from one definite index n and on...but not for ... ,The key part of this problem is to realize (1+1n)n≥2. We use the binomial theorem here: (1+1n)n≥1+n⋅1⋅1n=2. Now we apply our induction ... ,n!≥n(n−1)(n−2)(n−3)⋯⌈n/2⌉≥(⌈n/2⌉)⌈n/2⌉. ,2>nn. My work: I tried to apply induction. So, at the induction step, I need to prove, ,圖解連續正整數平方和公式. 附圖，由5個正方形與5個小長方形組合成大長方形，5個正方形的邊長分別是1、2、3、4、5，5個小長方形的邊長規格分別 ... ,n(n+1). 2. , 想找出12 + 22 + 32 + ··· + n2 求. 和的計算公式。由. (k + 1)3. − k ... n. ∑ k=1 k−n. = n3 +. 3. 2 n2 +. 1. 2 n. 即12+22+33 + ···+n2 =. ,我說:「好, 我就舉“對於每一個自然數n ≥ 5, 試證: 2n > n2”來說明。」 證明如下: “步驟一” n = 5 代入, 不等式左邊25 = 32, 不等式右邊52 = 25, 32 > ... ,下面用数学归纳法证明： （1）当n=5时，25＞52成立． （2）假设n=k（ ... ,n→∞ ln n n 。 (2) lim n→∞ ln n2. 5n2 。 (3) ...
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 N n 2 n 2 相關參考資料
Proof by induction: $2^n > n^2$ for all integer $n$ greater than ...
You proved it's true for n=5. Now suppose it's true for some integer n≥5. The aim is to prove it's true for n+1. But (♤)2n+1=2×2n>2×n2>(n+1)2. https://math.stackexchange.com Proof that $n^2 < 2^n$ - Mathematics Stack Exchange
n2<2n⟺2logn<nlog2⟺lognn<log22. But we know that lognn→n→∞0 , so the above inequality's definitely true from one definite index n and on...but not for ... https://math.stackexchange.com Prove $n! < (n2)^n$ by induction - Mathematics Stack Exchange
The key part of this problem is to realize (1+1n)n≥2. We use the binomial theorem here: (1+1n)n≥1+n⋅1⋅1n=2. Now we apply our induction ... https://math.stackexchange.com Prove that n!≥(⌈n2⌉)⌈n2⌉ [closed] - Math Stack Exchange
n!≥n(n−1)(n−2)(n−3)⋯⌈n/2⌉≥(⌈n/2⌉)⌈n/2⌉. https://math.stackexchange.com Show that if $n>2$, then - Mathematics Stack Exchange
2>nn. My work: I tried to apply induction. So, at the induction step, I need to prove, https://math.stackexchange.com 圖解連續正整數平方和公式- n - 昌爸工作坊
圖解連續正整數平方和公式. 附圖，由5個正方形與5個小長方形組合成大長方形，5個正方形的邊長分別是1、2、3、4、5，5個小長方形的邊長規格分別 ... http://www.mathland.idv.tw 數學歸納法教學一二
n(n+1). 2. , 想找出12 + 22 + 32 + ··· + n2 求. 和的計算公式。由. (k + 1)3. − k ... n. ∑ k=1 k−n. = n3 +. 3. 2 n2 +. 1. 2 n. 即12+22+33 + ···+n2 =. https://web.math.sinica.edu.tw 數學歸納法的證明
我說:「好, 我就舉“對於每一個自然數n ≥ 5, 試證: 2n > n2”來說明。」 證明如下: “步驟一” n = 5 代入, 不等式左邊25 = 32, 不等式右邊52 = 25, 32 > ... https://web.math.sinica.edu.tw 比较2n与n2的大小（n∈N*）_百度知道
下面用数学归纳法证明： （1）当n=5时，25＞52成立． （2）假设n=k（ ... https://zhidao.baidu.com 第9 章無窮級數(Infinite Series) 9.1 數列(Sequences)
n→∞ ln n n 。 (2) lim n→∞ ln n2. 5n2 。 (3) ... http://www.math.ntu.edu.tw |