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Showing that ratio $(4n^2 + 4n + 1)^n$ to $(4n^2 + 4n)^n$ is approximately $4n + 4$ to $4n + 3$

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#algebra-precalculus #taylor-expansion #binomial-coefficients #binomial-theorem #estimation
72
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Simplifying a cosine triple angle expansion

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#trigonometry #binomial-theorem
69
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binomial theorem combinatorics intuition

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#combinatorics #discrete-mathematics #intuition #binomial-theorem
107
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The 0 Exponent(s) in A Freshman's Dream Proof for Commutative Rings

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#abstract-algebra #ring-theory #binomial-theorem
82
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Binomial rule and repeatedly differentiating

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#real-analysis #derivatives #binomial-theorem
466
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Binomial expansion of x is large

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#binomial-theorem
736
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how to express the $n$th power of the cosine as a series of cosines?

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#trigonometry #exponentiation #binomial-theorem
210
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Ramanujan's q function

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#calculus #integration #summation #gamma-function #binomial-theorem
113
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Closed-form expression of $f(t)$ (using its Taylor series?)

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#ordinary-differential-equations #partial-differential-equations #taylor-expansion #binomial-theorem
147
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Relation between coefficients of $(x+1)^n$ and choosing $k$ elements from a set ot size $n$?

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#binomial-coefficients #binomial-theorem
30
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Proving $ \sum_{x \in A} x^k = \sum_{x \in B} x^k $ for a partitioning of a specific set.

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#number-theory #induction #binomial-theorem
75
Views

Is it possible to simplify this sum? (maybe an integral representation?)

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#sequences-and-series #power-series #taylor-expansion #binomial-theorem
124
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How do I separate imaginary and real terms of Cartesian Coordinates of finite complex geometric sum?

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#complex-numbers #summation #vectors #binomial-theorem #geometric-series
74
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Can I use the binomial theorem to expand (1+n)^n?

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#binomial-theorem
75
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Solve $(n+1)^k-1=n!$

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#number-theory #diophantine-equations #factorial #binomial-theorem

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