N^2 2^n
It is called the generating function of the sequence of square numbers, and it can be obtained without calculus. [math]-displaystyle -begin matrix} - ...,Theorem: For any natural number n ≥ 5, n2 < 2n. Proof: By induction on n. As a base case, if n = 5, then we have that 52 = 25 < 32 = 25, so the claim holds ... ,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. ,First since one must have n≠3, the induction base must be n=4. For the induction step: Suppose n2≤2n. Then, (n+1)2=n2+2n+1≤2n+2n+1≤2n+2n=2n+1. ,Hint only: For n≥3 you have n2>2n+1 (this should not be hard to see) so if n2<2n then consider 2n+1=2⋅2n>2n2>n2+2n+1=(n+1)2. ,关于1^2+2^2+3^2+…+n^2的多种推导证明方法- 关于前n 个自然数的平方和公式的证明方法湘西州花垣县边城高级中学-张秀洲在《数列》教学过程中，大家都能熟练掌握前n 个自 ... ,猜想：当n≥5时，2n＞n2． 下面用数学归纳法证明： （1）当n=5时，25＞52成立．
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 N^2 2^n 相關參考資料
How do you evaluate the sum of (n^2)(2^n) from n=1 to infinity?
It is called the generating function of the sequence of square numbers, and it can be obtained without calculus. [math]-displaystyle -begin matrix} - ... https://www.quora.com Mathematical Induction
Theorem: For any natural number n ≥ 5, n2 < 2n. Proof: By induction on n. As a base case, if n = 5, then we have that 52 = 25 < 32 = 25, so the claim holds ... https://web.stanford.edu 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 of $n^2 leq 2^n$. - Mathematics Stack Exchange
First since one must have n≠3, the induction base must be n=4. For the induction step: Suppose n2≤2n. Then, (n+1)2=n2+2n+1≤2n+2n+1≤2n+2n=2n+1. https://math.stackexchange.com Proof that $n^2 < 2^n$ - Mathematics Stack Exchange
Hint only: For n≥3 you have n2>2n+1 (this should not be hard to see) so if n2<2n then consider 2n+1=2⋅2n>2n2>n2+2n+1=(n+1)2. https://math.stackexchange.com 关于1^2+2^2+3^2+…+n^2的多种推导证明方法 - 百度文库
关于1^2+2^2+3^2+…+n^2的多种推导证明方法- 关于前n 个自然数的平方和公式的证明方法湘西州花垣县边城高级中学-张秀洲在《数列》教学过程中，大家都能熟练掌握前n 个自 ... https://wenku.baidu.com 比较2n与n2的大小（n∈N*） - 百度知道
猜想：当n≥5时，2n＞n2． 下面用数学归纳法证明： （1）当n=5时，25＞52成立． https://zhidao.baidu.com |