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Combined display of all available logs of ProofWiki. You can narrow down the view by selecting a log type, the username (case-sensitive), or the affected page (also case-sensitive).
- 16:49, 29 February 2024 Asdfghjklohhnhn talk contribs created page Closed Form for Triangular Numbers/Combinatorial Proof (Created page with "== Theorem == {{:Closed Form for Triangular Numbers}} == Combinatorial Proof == <onlyinclude> Suppose we have $n + 1$ people who all shake hands with each other person once then we can count how many handshakes occur by counting the handshakes of each person, the first person shakes hands with all other $n$ people, then the second person shakes hands with the remaining $n - 1$ people, which continues until the $n$-th person can only shake hands with the $(n + 1)$-th per...")
- 15:32, 29 February 2024 Asdfghjklohhnhn talk contribs created page Sum of First n Consecutive Integers (Created page with "== Theorem == <onlyinclude> :$\ds \sum_{i \mathop = 0}^n i = \frac{n(n - 1)}{2}$ </onlyinclude> == Proof 1 == {{:Sum of First n Consecutive Integers/Proof 1}}")
- 07:20, 27 December 2023 Asdfghjklohhnhn talk contribs created page Template:Symmetric Integral of Even Function over One Plus Even Function to Power of Odd Function/Proof (Created page with "== Theorem == {{:Symmetric Integral of Even Function over One Plus Even Function to Power of Odd Function}} == Proof == <onlyinclude> Let the integrand be denoted by $f(x) = \frac{e(x)}{1 + t(x)^{o(x)}}$. $f(x)$ can be broken into the sum of two functions $E(x)$ and $O(x)$ defined as follows: $$E(x) = \frac{f(x) + f(-x)}{2}$$ $$O(x) = \frac{f(x) - f(-x)}{2}$$ It is clear that $E(x)$ is an even function by the {{Defof|Even Function}}: $F(x) = F(-x)$ which can be verifi...")
- 07:11, 27 December 2023 Asdfghjklohhnhn talk contribs created page Symmetric Integral of an Even Function over the Quantity One Plus an Even Function to the Power of an Odd Function/Proof (Created page with "== Theorem == {{:Symmetric Integral of an Even Function over the Quantity One Plus an Even Function to the Power of an Odd Function}} == Proof == <onlyinclude> Let the integrand be denoted by $f(x) = \frac{e(x)}{1 + t(x)^{o(x)}}$. $f(x)$ can be broken into the sum of two functions $E(x)$ and $O(x)$ defined as follows: $$E(x) = \frac{f(x) + f(-x)}{2}$$ $$O(x) = \frac{f(x) - f(-x)}{2}$$ It is clear that $E(x)$ is an even function by the {{Defof|Even Function}}: $F(x) =...")
- 06:04, 27 December 2023 Asdfghjklohhnhn talk contribs created page Symmetric Integral of an Even Function over the Quantity One Plus an Even Function to the Power of an Odd Function (Created page with "== Theorem == <onlyinclude> :$\ds \int_{-a}^a \frac{e(x)}{1 + t(x)^{o(x)}} dx = \int_0^a e(x)dx$ where $a$ is a positive real number, $e(x)$ and $t(x)$ are arbitrary even functions, and $o(x)$ is an arbitrary odd function. <onlyinclude> == Proof == {{:Symmetric Integral of an Even Function o...") Tag: Visual edit: Switched
- 16:11, 15 December 2023 Asdfghjklohhnhn talk contribs created page Sum of nth Fibonacci Number over nth Power of 2 (Created page with "== Theorem == <onlyinclude> $$\sum_{n = 0}^{\infty} \frac{F_n}{2^n} = 2$$ Where $F_n$ is the $n$-th Fibonacci number. == Proof 1 (Using a Sample Space of Probabilities) == Let us define a Sample Space which satisfies the Kolmogorov Axioms such that it is the set of all combinations of flipping a fair coin until you receive two heads in a row. === Sum of nth Fibonac...") Tag: Visual edit: Switched