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- Why is $1^{\\infty}$ considered to be an indeterminate form
The indeterminate forms are often abbreviated with stuff like "$1^\infty$" but that's not what they mean This "$1^\infty$" (in regards to indeterminate forms) actually means: when there is an expression that approaches 1 and then it is raised to the power of an expression that approaches infinity we can't determine what happens in that form
- Why is $1$ not a prime number? - Mathematics Stack Exchange
actually 1 was considered a prime number until the beginning of 20th century Unique factorization was a driving force beneath its changing of status, since it's formulation is quickier if 1 is not considered a prime; but I think that group theory was the other force
- I have learned that 1 0 is infinity, why isnt it minus infinity?
Thus the idea of $\frac{1}{0}$ can be interpreted as saying that if $\epsilon$ is infinitesimal then $\frac{1}{\epsilon}$ is infinite This resolves your problem because it shows that $\frac{1}{\epsilon}$ will be positive infinity or infinite infinity depending on the sign of the original infinitesimal, while division by zero is still undefined
- Double induction example: $ 1 + q + q^2 - Mathematics Stack Exchange
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- General term formula of series 1 1 + 1 2 + 1 3 . . . +1 n
$$\ln(n+1)\le\sum_{i=1}^n\frac1i\le\ln(n)+1$$ This is a rather tight upper limit and lower limit you can use to approximate your answer One could also note that $$\sum_{i=1}^n\frac1i=\int_0^1\sum_{i=0}^{n-1}x^i\ dx=\int_0^1\frac{1-x^n}{1-x}\ dx$$ We also have the Euler-Maclaurin expansion:
- Word，插入多级列表，但是改了1. 1，第二章的2. 1也变成1. 1，随着改变而改变，这种情况怎么处? - 知乎
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