Reputation
15,476
Top tag
Next privilege 20,000 Rep.
Access 'trusted user' tools
Badges
2 31 75
Newest
 Nice Answer
Impact
~476k people reached

Jul
13
awarded  Nice Answer
Jul
4
comment Arrangement of any number of objects from $n$ objects
$\sum_{r = 0}^n \frac{1}{(n-r)!} = \sum_{k = 0}^n \frac{1}{k!}$, which is surprisingly close to $\sum_{k = 0}^\infty \frac{1}{k!}$
Jun
30
awarded  Nice Answer
Jun
11
comment A planar graph on $n \geq 3$ vertices has at most $3n-6$ edges: is the converse true?
Producing a drawing of a graph in the plane with no edge crossings is a perfectly legitimate way to demonstrate planarity. Kuratowski's theorem is nice if such a drawing is difficult to produce.
May
30
accepted Multiplication Principle and Inclusion-Exclusion: $2^n = \sum_{i = 0}^n (-1)^i \binom{n}{i} \binom{2n - 2i}{n - 2i}$
May
30
revised Multiplication Principle and Inclusion-Exclusion: $2^n = \sum_{i = 0}^n (-1)^i \binom{n}{i} \binom{2n - 2i}{n - 2i}$
editing to change my vote
May
30
comment Multiplication Principle and Inclusion-Exclusion: $2^n = \sum_{i = 0}^n (-1)^i \binom{n}{i} \binom{2n - 2i}{n - 2i}$
I don't know why I've been so dense with this identity. I see you are correct now. Thank you.
May
28
revised Why is Infinity multiplied by Zero not an easy Zero answer?
deleted 1 character in body
May
28
comment Multiplication Principle and Inclusion-Exclusion: $2^n = \sum_{i = 0}^n (-1)^i \binom{n}{i} \binom{2n - 2i}{n - 2i}$
Thanks for the enlightening answers. Perhaps I'll finally learn to turn to complex methods for binomial sums.
May
27
asked Multiplication Principle and Inclusion-Exclusion: $2^n = \sum_{i = 0}^n (-1)^i \binom{n}{i} \binom{2n - 2i}{n - 2i}$
May
26
reviewed Approve Determining how many combinations there are when every item has a pair it can't exist with.
May
26
comment For which $x\in\mathbb{R}$ is the series of general term $a_n = x^{n!}$ convergent?
Try comparing the behavior of $\sum_{n = 0}^\infty x^{n!}$ with $\sum_{n = 0}^\infty x^n$.
May
26
revised Showing $\lbrace (x,y) \in \mathbb{R}^2:xy=1 \rbrace$ is Closed
deleted 69 characters in body; edited title
May
22
awarded  Yearling
May
22
comment Find $\lim_{x\rightarrow\infty}\sin^2(x^2)$
@bws It sounds great, but I would add that $f(a_n)$ does not just tend toward 0, it is equal to 0 for all $n$. Similarly for $f(b_n)$.
May
22
answered Find $\lim_{x\rightarrow\infty}\sin^2(x^2)$
May
22
revised Taylor series $\ln(1+e^x)$ about $x=0$
added 3 characters in body
May
20
answered Number of ways to place $K$ objects in $N^3$ cube
May
20
answered Understanding the set of neighbors of a set
May
12
answered If every compact set is closed, then is the space Hausdorff?