For questions about recurrence relations, convergence tests, and identifying sequences. For questions on finite sums use the (summation) instead.

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8
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1answer
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+50

Intuition behind proof of bounded convergence theorem in Stein-Shakarchi

Theorem 1.4 (Bounded convergence theorem) Suppose that $\{f_n\}$ is a sequence of measurable functions that are all bounded by $M$, are supported on a set $E$ of finite measure, and $f_n(x) \to f(x)$ ...
3
votes
0answers
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+50

Explicit solutions to a digamma function equation

My main question: Can we obtain the exact solutions from the following equation? $$ \sum_{k=1}^{n}\cfrac{1}{k-x-1}=0 $$ Notation: This problem was reached from the digamma function $\psi$ as ...
3
votes
2answers
260 views
+50

The relationship between tan(x) and square roots

Please note: I am working in DEGREES I think the easiest way to illustrate my point is by showing some examples: $ \tan(0^\circ) = \sqrt 0 = 0$ $ \tan(22.5^\circ) = \sqrt 2 -1$ $ 3 \cdot \tan(30 ^...
0
votes
1answer
83 views
+100

Having no derangements — any advantage?

Is there any problem-solving advantage when a sequence has no derangements? Edit Perhaps the non-derangements are just a by-product of the argument that we find primes in $(m-k,k] \iff k|m$? In an ...