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Prove that $1 < \sum\limits_{n = 1001}^{3001} \frac 1 n < \frac 3 2.$

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#real-analysis #integration #summation #solution-verification #approximation
60
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A step in the proof of Erdos-Tetali Lemma.

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#probability #summation #proof-explanation #extremal-combinatorics #probabilistic-method
87
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If $abc=1$, then how do you prove $\frac{b-1}{bc+1}+\frac{c-1}{ac+1}+\frac{a-1}{ab+1} \geq 0$?

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#inequality #summation #rearrangement-inequality #tangent-line-method
360
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Alternating sum of combinatorics

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#combinatorics #summation #binomial-coefficients
47
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Understanding the Big-O of this summation

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#summation #asymptotics
385
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Transforming a summation over multiple variables with a condition

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#algebra-precalculus #summation
341
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Change of variables in a sum

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#calculus #summation #change-of-variable
49
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Convergence of a sum similar to Parseval's Indentity

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#real-analysis #summation #parsevals-identity
412
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Double sum over random variables and Wald's equation

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#probability #summation #random-variables #expected-value
51
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Summation involving 2 variables

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#calculus #algebra-precalculus #summation
79
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Behaviour of sine sums

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#trigonometry #summation #intuition
29
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Find number of polynomials of given form with positive zeroes

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#polynomials #summation
98
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Can we find a closed form for $\sum _{i=0}^{\infty } ((-1)^{i}x^i\prod_{j=1}^{i}\frac{e^j}{e^j-1})$?

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#sequences-and-series #summation #closed-form #infinite-product
370
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Proving a combinatoric statement with a committee forming argument

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#combinatorics #summation #binomial-coefficients #combinatorial-proofs
165
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Derivation of pressure using partition function

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#derivatives #summation #partial-derivative

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