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 71 How come $32.5 = 31.5$? 25 Finding $\sum\limits_{n=2}^\infty \ln\left(1-\frac{1}{n^2}\right)$ 9 Infinite series question requiring no explanation 6 Prove that the sequence given by $c_n = \sqrt{1+c_{n-1}}$ converges and find the limit 5 Find $\sum\limits_{n=1}^{\infty}\frac{n^4}{4^n}$

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 +10 incremental computation of standard deviation +10 Change of variable using dirac delta function +5 Connection between the Laplace transform and generating functions +10 rewrite $\frac{\partial \theta}{\partial t}=k \frac{\partial^2 \theta}{\partial x^2}$ as a DE with two new variables $q_1$ and $q_2$

Questions (8)

 32 Evaluating the infinite series $\sum\limits_{n=1}^\infty(\sin\frac1{2n}-\sin\frac1{2n+1})$ 24 Connection between the Laplace transform and generating functions 7 Closed-form expression for $\sum_{k=0}^n\binom{n}kk^p$ for integers $n,\,p$ 3 Compute the value of $\sum\limits_{k=1}^{100}\left|\bigcup_{i=1}^k A_i\right|$ 2 Finding the least rational $r>0$ such that $\prod_{n=0}^3(2\cos(2^n\pi r)-1)=1$

Tags (99)

 74 recreational-mathematics × 2 36 summation × 5 71 fake-proofs 20 differential-equations × 13 71 geometry 18 limits × 16 44 calculus × 28 16 algebra-precalculus × 10 37 sequences-and-series × 15 15 linear-algebra × 12

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