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 63 How come $32.5 = 31.5$? 22 Finding the sum of a series of natural logs 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 How to solve for u(x,t)?

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 +10 What is the rank of the differentiation operator on Pn? What is the kernel? +5 Evaluating the infinite series $\sum\limits_{n=1}^\infty(\sin\frac1{2n}-\sin\frac1{2n+1})$ +20 How come $32.5 = 31.5$? +5 Connection between the Laplace transform and generating functions

### Questions (8)

 32 Evaluating the infinite series $\sum\limits_{n=1}^\infty(\sin\frac1{2n}-\sin\frac1{2n+1})$ 20 Connection between the Laplace transform and generating functions 6 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 (84)

 66 recreational-mathematics × 2 28 sequences-and-series × 11 63 fake-proofs 17 differential-equations × 11 63 geometry 16 limits × 16 43 calculus × 29 14 algebra-precalculus × 9 31 summation × 4 10 pde × 4

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