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Apr
23
revised Möbius sums and Eulers totient function
added 3 characters in body
Mar
29
revised Summations involving $\sum_k{x^{e^k}}$
added 2 characters in body
Mar
11
answered Summations involving $\sum_k{x^{e^k}}$
Mar
11
revised How find that $\left(\frac{x}{1-x^2}+\frac{3x^3}{1-x^6}+\frac{5x^5}{1-x^{10}}+\frac{7x^7}{1-x^{14}}+\cdots\right)^2=\sum_{i=0}^{\infty}a_{i}x^i$
added 12 characters in body
Mar
11
comment $\sum_{n=1}^\infty \frac{n!}{n^n}$
For similar identities see: en.wikipedia.org/wiki/Sophomore%27s_dream
Mar
11
comment $\sum_{n=1}^\infty \frac{n!}{n^n}$
Also note that: $$\int_{0}^1 n(-x\log(x))^{n-1} dx=\frac{n!}{n^n}$$ $$\int_{0}^1\frac{1}{(x\ln(x)+1)^2}dx=\int_{0}^1 \sum_{n=1}^\infty n(-x\log(x))^{n-1} dx=\sum_{n=1}^\infty\frac{n!}{n^n}$$
Mar
10
answered Find an asymptotic formula for $\sum\limits_{n\leq x} d(n)\log n$
Feb
22
awarded  Popular Question
Feb
18
reviewed Approve Norm of orthogonal projection
Feb
17
revised Why doesn't Mertens's second theorem prove the Prime Number Theorem?
added 3 characters in body
Feb
15
comment Proving $\sum_{n=0}^{\infty }\frac{\sin^4(4n+2)}{(2n+1)^2}=\frac{5\pi ^2}{16}-\frac{3\pi }{4}$
Probably can be explained through some Fourier series expansion.
Feb
14
answered What is the value of $\sum_{p\le x} 1/p^2$?
Feb
12
comment How to re-learn math: books or websites?
The question is really vague, it might help if you were more specific about your situation.
Feb
12
comment Limit of $(\cos{xe^x} - \ln(1-x) -x)^{\frac{1}{x^3}}$
You don't need to write approximately all your statements involving big O notation are correct.
Feb
12
comment Limit at infinity of a bounded function
Note this is only true because $\lim_{x\to\infty}xf'(x)$ does not exist, this is because the cosine function appearing in $f'(x)$ constantly oscillates and prevents the limit from converging to a fixed value. However if his limit does exist, then it will always be zero.
Feb
12
answered Limit at infinity of a bounded function
Feb
12
reviewed Approve Greatest of three random variables
Feb
12
comment Do four natural numbers exist which satisfy these constraints?
@JohnWO I don't understand what you're saying
Feb
12
revised Do four natural numbers exist which satisfy these constraints?
added 36 characters in body; edited title
Feb
5
comment If $\sum_{n_0}^{\infty} a_n$ diverges prove that $\sum_{n_0}^{\infty} \frac{a_n}{a_1+a_2+…+a_n} = +\infty $
@onlyme I was thinking of something similar.