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Show $p(x_n)$ $\rightarrow$ $p(x)$ for a convergent sequence $\{ x_n \}$

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#real-analysis #sequences-and-series #proof-verification #polynomials #proof-writing
396
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The convergence of the sequence $(1/(n^a\ln^b(n)))$, where $a,b\in\mathbb{R}$

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#sequences-and-series #proof-verification #convergence-divergence
175
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Prove that $\sum_{j=0}^{\infty}(-1)^j\left(\frac{1}{5+6j}+\frac{1}{1+6j} \right) = \frac{\pi}{3}$

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#sequences-and-series #definite-integrals #improper-integrals
297
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Double fractional part integral

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#integration #sequences-and-series #definite-integrals #fractional-part
164
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Can someone help me with proving the convergence of a sequence written in this form?

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#real-analysis #sequences-and-series
50
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Help in understanding arithmetic form of Euler's proof of infinite primes.

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#sequences-and-series #prime-numbers #arithmetic #proof-explanation
3.3k
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No convergent sequence containing infinitely many ones can have a limit other than one.

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#real-analysis #sequences-and-series #proof-verification
252
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Solve Recurrence Relation $a_k=(a_{k-1})^2-2$

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#sequences-and-series #recurrence-relations #infinite-product
1.9k
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Proving a sequence with infinitely many zeros is not zero heavy?

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#real-analysis #sequences-and-series #proof-verification
433
Views

Limit superior of a sequence of oscillating functions related to Chebyshev polynomials

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#sequences-and-series #functions #polynomials #limsup-and-liminf #chebyshev-polynomials
112
Views

Evaluation of a series involving the harmonic number

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#sequences-and-series #zeta-functions #euler-mascheroni-constant #euler-sums
627
Views

Series of Geometric Means Converges

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#sequences-and-series #analysis
761
Views

Evaluating $\sum_{k=1}^{\infty} 2\ln{(2k)} - \ln{(2k-1)} - \ln{(2k+1)} $

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#calculus #sequences-and-series
64
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Prove that a sequence converges

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#real-analysis #sequences-and-series #proof-writing #uniform-convergence #cauchy-sequences
555
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Isolating Exponent Variables for Deriving Equations

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#sequences-and-series #derivatives #exponentiation

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