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 Apr23 revised Möbius sums and Eulers totient function added 3 characters in body Mar29 revised Summations involving $\sum_k{x^{e^k}}$ added 2 characters in body Mar11 answered Summations involving $\sum_k{x^{e^k}}$ Mar11 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 Mar11 comment $\sum_{n=1}^\infty \frac{n!}{n^n}$ For similar identities see: en.wikipedia.org/wiki/Sophomore%27s_dream Mar11 comment $\sum_{n=1}^\infty \frac{n!}{n^n}$ Also note that: $$\int_{0}^1 n(-x\log(x))^{n-1} dx=\frac{n!}{n^n}$$ $$\int_{0}^1\frac{1}{(x\ln(x)+1)^2}dx=\int_{0}^1 \sum_{n=1}^\infty n(-x\log(x))^{n-1} dx=\sum_{n=1}^\infty\frac{n!}{n^n}$$ Mar10 answered Find an asymptotic formula for $\sum\limits_{n\leq x} d(n)\log n$ Feb22 awarded Popular Question Feb18 reviewed Approve Norm of orthogonal projection Feb17 revised Why doesn't Mertens's second theorem prove the Prime Number Theorem? added 3 characters in body Feb15 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. Feb14 answered What is the value of $\sum_{p\le x} 1/p^2$? Feb12 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. Feb12 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. Feb12 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. Feb12 answered Limit at infinity of a bounded function Feb12 reviewed Approve Greatest of three random variables Feb12 comment Do four natural numbers exist which satisfy these constraints? @JohnWO I don't understand what you're saying Feb12 revised Do four natural numbers exist which satisfy these constraints? added 36 characters in body; edited title Feb5 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.