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 15 Find $\lim\limits_{n \rightarrow \infty}\dfrac{\sin 1+2\sin \frac{1}{2}+\cdots+n\sin \frac{1}{n}}{n}$ 13 Evaluating $\int \frac{1}{{x^4+1}} dx$ 11 Evaluating $\sum\limits_{k=1}^{\infty}\frac1{(3k+1)(3k+2)}$ 8 $f'(x)=f(x)$ and $f(0)=0$ implies that $f(x)=0$ formal proof 8 Find $\sum\limits_{k\, \text{ odd}} \frac{2(k^2-1)}{k^4+k^2+1}$

### Reputation (2,442)

 +10 Why don't Venn diagrams count as formal proofs? +10 Question about finding minimum-Hilbert spaces +5 How to solve $y(y'+3)=ax^2+bx+c, \quad a,b,c \in \mathbb{R}$ +10 Find $\lim\limits_{n \rightarrow \infty}\dfrac{\sin 1+2\sin \frac{1}{2}+\cdots+n\sin \frac{1}{n}}{n}$

### Questions (19)

 25 Evaluate $\sum\limits_{k=1}^{\infty} \frac{k^2-1}{k^4+k^2+1}$ 12 Using $\bigvee$ and $\bigwedge$ instead $\exists$ and $\forall$ 8 How to evaluate $\sum\limits_{k=0}^{n} \sqrt{\binom{n}{k}}$ 8 How to show that $(\mathbb{Q}(\sqrt{2}))^{\times} \cong (\mathbb{Q}(\sqrt{3}))^{\times}$ 6 How to solve $y(y'+3)=ax^2+bx+c, \quad a,b,c \in \mathbb{R}$

### Tags (56)

 40 calculus × 10 14 complex-analysis × 9 35 real-analysis × 14 9 analysis × 3 28 sequences-and-series × 7 8 linear-algebra × 2 27 integration × 6 6 differential-equations × 7 18 limits × 2 6 determinant

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 Mathematics 2,442 rep 1030 TeX - LaTeX 402 rep 311