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 12 What test can be used to show $\sum \dfrac{n!}{n^n}$ converges? 9 Proving equivalences between prime counting functions. 8 What is the name of this function $f(x) = \frac{1}{1+x^n}$? 8 Prove that $(a+1)(a+2)…(a+b)$ is divisible by $b!$ 7 Is there any function that has the series expansion $x+x^{\frac{1}{2}}+x^{\frac{1}{3}}+\cdots$?

### Reputation (5,265)

 +5 Möbius sums and Eulers totient function +10 What is the value of $\sum_{p\le x} 1/p^2$? +10 Find an asymptotic formula for $\sum\limits_{n\leq x} d(n)\log n$ +5 On a long proof

### Questions (103)

 46 On a long proof 24 Series of Cyclotomic polynomials 21 Academic integrity [closed] 17 Large integer help 15 Undergraduate Schools for Mathematics

### Tags (115)

 71 number-theory × 57 29 real-analysis × 12 69 sequences-and-series × 50 23 limits × 14 56 elementary-number-theory × 34 20 summation × 15 49 calculus × 26 18 prime-numbers × 21 40 analytic-number-theory × 21 15 complex-analysis × 8

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