daniel.jackson
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### Questions (38)

 10 If $(a_{n})$ is increasing, is $u_{n}=\frac{a_{1}+\cdots+a_{n}}{n}$ increasing as well? 10 Given $a_{1}=1, \ a_{n+1}=a_{n}+\frac{1}{a_{n}}$, find $\lim \limits_{n\to\infty}\frac{a_{n}}{n}$ 10 Basic Taylor expansion question 9 if $\int_1^{\infty}f(x)\ \mathrm dx$ converges, must $\int_1^{\infty}f(x)\sin x\ \mathrm dx$ converge? 9 Does $\sum \limits_{n=1}^\infty\frac{\sin n}{n}(1+\frac{1}{2}+\cdots+\frac{1}{n})$ converge (absolutely)?

### Reputation (1,101)

 +5 sin(n) subsequence limits set +10 if $\int_1^{\infty}f(x)\ \mathrm dx$ converges, must $\int_1^{\infty}f(x)\sin x\ \mathrm dx$ converge? +5 Basic Taylor expansion question +5 Adjoint of a linear transformation in an infinite dimension inner product space

 12 Given $a_{1}=1, \ a_{n+1}=a_{n}+\frac{1}{a_{n}}$, find $\lim \limits_{n\to\infty}\frac{a_{n}}{n}$ 4 Does $\int_0^\infty |\cos(x^2)| \mathrm dx$ converge? 1 Is this language context-free? 1 For which values of $\alpha, \beta$, $\int_0^1 \frac{\ln^\alpha(1+x)}{x^\beta(1-x)^\alpha}\mathrm dx$ exists? 0 Divergence of an improper integral - |cos(x^2)|/x^q

### Tags (13)

 13 calculus × 25 1 formal-languages 12 sequences-and-series × 16 0 linear-algebra × 12 4 integration × 4 0 taylor-expansion × 3 1 improper-integrals × 5 0 real-analysis × 2 1 context-free-grammar × 2 0 quadratic-forms × 2

### Accounts (11)

 Mathematics 1,101 rep 821 TeX - LaTeX 253 rep 17 Computer Science 251 rep 16 Stack Overflow 248 rep 36 Area 51 151 rep