The series does not converge, because as you observe, the partial sums $1,0,1,0,\ldots$ oscillate and do not approach a single limit. There are various ways to assign values to some divergent series, …

Jan 15, 2013 · Possible Duplicate: How do I convince someone that $1+1=2$ may not necessarily be true? I once read that some mathematicians provided a very length proof of $1+1=2$. Can you think …

@coffeemath Debatable: you can write Hn = S2 n + 1 n! Where S denotes Stirling numbers of the first kind. But it may not be considered a "closed form", since Stirling numbers are not much more easy …

Possible Duplicate: Prove 0! = 1 0! = 1 from first principles Why does 0! = 1 0! = 1? All I know of factorial is that x! x! is equal to the product of all the numbers that come before it. The product of 0 and …

5 One can write 1 + 1 2 + 1 3 + ⋯ + 1 n = γ + ψ(n + 1) 1 + 1 2 + 1 3 + + 1 n = γ + ψ (n + 1) where γ γ is Euler's constant and ψ ψ is the digamma function. Of course, one reason for creating the digamma …

Nov 28, 2019 · Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant …

I'm working on a double induction problem with the following prompt: Prove by induction on n n that for any real number q> 1 q> 1 and integer n ≥ 0 n ≥ 0:

$ (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 …

Jun 26, 2020 · 对于 (1+1/n)^n ＜ 3的证明如下图 (图片来自 崔尚斌数学分析教程)

This number is 0 0. So for any number k k, you have k ⋅0x = 0 =0x k 0 x = 0 = 0 x, hence you cannot say that the equation 00 ⋅0x =0x 0 0 0 x = 0 x suggests that 00 0 0 "should" be 1 1. The second argument …