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Easy way to remember Taylor Series for log (1+x)?
Assuming $|x|<1$, if one can easily remember that $$ \\dfrac{1}{1-x}=\\sum_{n=0}^{\\infty}x^{n} $$ then one can derive the following \\begin{eqnarray*} \\mbox{log ...
probability - Expectation on 1/X - Mathematics Stack Exchange
Expectation on 1/X Ask Question Asked 13 years, 11 months ago Modified 4 years, 9 months ago
一个最大值大于1的概率密度函数的意义是什么？ - 知乎
题主应该是把 概率质量函数 （probability mass function）和 概率密度函数 （probability density function）搞混了。 概率质量函数的取值确实无法大于1，但概率密度函数则不然。 以下内容搬运自维基百科： 在概率论中，概率质量函数是离散随机变量在各特定取值上的概率。
足球让球0.5/1什么意思？ - 知乎
把 里面的“/” 理解为将投注额平分。 比如你打算投注10块的让0.5/1， 就是5块买 让0.5 剩下5块买让1 如果让球方净胜1球，那么让0.5的5块你赢了，让1的5块不输不赢，总的就赢一半 如果让球方净胜2球及以上，那么让0.5的赢了，让1的也赢了，总的就全赢 如果平局或者让球方输球，那么让0.5的输了，让1 ...
linear algebra - Showing that $l_2$ norm is smaller than $l_1 ...
Here is a proof that works for any norm on a finite dimensional vector space, not just ℓN p norms for p ∈ [1, ∞). Assume wlog that {ei}Ni = 1 is a basis such that ‖ei‖ = 1. (if not you can choose a new basis by normalizing the basis vectors.) In RN, you can choose the unit vectors along coordinate axes.
Why is 1 raised to infinity Not defined and not "1" [duplicate]
$1$ square is $1$, so is raised $1$ to $123434234$. My maths teacher claims that $1$ raised to infinity is not $1$, but not defined. Is there any reason for this? I know that any number raised to
Simplify K!/ (K+1)! - Mathematics Stack Exchange
Pretend K=3 That means (K+1)= 4 This means you'd be dividing 3*2*1 by 4*3*2*1. Consider how you'd cancel out multiples by dividing them. Like how (2 (5+x))/2 would just equal 5+x. Following that idea we'd pretty much be able to cancel out every number in the numerator, so long as its also in the denominator. This would end up canceling every number except for 4 which equals (K+1). Essentially ...
Divergence of series sin(1/n) - Mathematics Stack Exchange
More accurately sin x∼0 x sin x ∼ 0 x $\mathrm{sin}x{\sim }_{0}x$ (in the sense of equivalence of functions near 0 0 $0$).
Integral $\\int \\sqrt{1+x^2}dx$ - Mathematics Stack Exchange
I was trying to do this integral $$\\int \\sqrt{1+x^2}dx$$ I saw this question and its' use of hyperbolic functions. I did it with binomial differential method since the given integral is in a form o...
Why Markov matrices always have 1 as an eigenvalue
qp=q where p is prob state transition matrix this means Y = 1 as an eigen vector of P' which also means There is an unique probability vector q which is an eigenvector associated with eigenvalue 1.
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