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Sum $sum_{(k_1, k_2, k_3): k_1+k_2+k_3=K, ,, n_1+n_2+n_3=N}k_1^{n_1}times k_2^{n_2} times k_3^{n_3}$

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bernoulli numbers bernoulli polynomials combinatorics elementary number theory number theory

Tangent Bundle of Product Manifold

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Partial Sums of Geometric Series

5 Mathematics Asked on 01/05/2022

analysis convergence divergence real analysis sequences and series summation

What does it really mean for a model to be pointwise definable?

1 Mathematics Asked on 01/05/2022

first order logic logic meta math model theory set theory

Line Integral gives no work done?

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calculus integration line integrals multivariable calculus

Show that if a Banach space is generated by a countable set with finite dimension then it has finite dimension

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banach spaces functional analysis

Can $a bmod 3$ be represented arithmetically without the mod or other integer-related functions?

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computational complexity modular arithmetic number theory

When is $sum_{i=1}^{m}i^n =0 bmod dfrac{m(m+1)}{2}$?

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divisibility elementary number theory number theory sequences and series

Define $X_n=sum_{k=1}^n kx_k$ and $Y_n=sum_{k=1}^n ky_k$. Prove that there exists an $n$ such that $X_n<Y_n$.

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convergence divergence measure theory real analysis

How find the solution to $ sum_{i=1}^{infty} left( frac{1}{2} right)^i left( frac{1}{i}right)$?

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sequences and series

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