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- 1 8, 1 4, 1 2, 3 4,7 8英寸分别是多少厘米? - 知乎
把1英寸分成8等分: 1 8 1 4 3 8 1 2 5 8 3 4 7 8 英寸。 This is an arithmetic sequence since there is a common difference between each term In this case, adding 18 to the previous term in the sequence gives the next term In other words, an=a1+d (n−1) Arithmetic Sequence: d=1 8
- Double induction example: $ 1 + q - Mathematics Stack Exchange
Slightly relevant: you can see my answer on this thread for a proof that uses double induction (just to get you exposed to how the mechanics of a proof using double induction might work)
- 想请大神给小白科普一下音频声道的专业知识，什么是2. 1声道、5. 1声道、7. 1声道?
5 1声道的第一次使用，追溯到1976年，当时杜比实验室修改了Todd-AO 70毫米胶片上6个类比音轨的使用方式，但当时在电影《洛根的逃亡》中杜比实验室的光学矩阵编码系统中，没有使用独立的环绕声，因此还不是真正的5 1，杜比实验室第一次在70毫米胶片中使用
- Why is $1 i$ equal to $-i$? - Mathematics Stack Exchange
11 There are multiple ways of writing out a given complex number, or a number in general Usually we reduce things to the "simplest" terms for display -- saying $0$ is a lot cleaner than saying $1-1$ for example The complex numbers are a field This means that every non-$0$ element has a multiplicative inverse, and that inverse is unique
- 知乎 - 有问题，就会有答案
知乎是一个中文互联网高质量问答社区和创作者聚集的原创内容平台，致力于分享知识、经验和见解，帮助用户找到答案。
- factorial - Why does 0! = 1? - Mathematics Stack Exchange
Intending on marking as accepted, because I'm no mathematician and this response makes sense to a commoner However, I'm still curious why there is 1 way to permute 0 things, instead of 0 ways
- 1 1+1 2+1 3+1 4+……+1 n=？怎么个解法？ - 知乎
两边求和，我们有 ln (n+1)<1 1+1 2+1 3+1 4+……+1 n 容易的， \lim _ {n\rightarrow +\infty }\ln \left ( n+1\right) =+\infty ，所以这个和是无界的，不收敛。
- Formula for $1^2+2^2+3^2+. . . +n^2$ - Mathematics Stack Exchange
$ (n+1)^3 - n^3 = 3n^2+3n+1$ - so it is clear that the $n^2$ terms can be added (with some lower-order terms attached) by adding the differences of cubes, giving a leading term in $n^3$ The factor 1 3 attached to the $n^3$ term is also obvious from this observation
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