# Tagged Questions

For questions about mathematical induction, a method of mathematical proof. Mathematical induction generally proceeds by proving a statement for some integer, called the *base case*, and then proving that if it holds for one integer then it holds for the next integer. This tag is primarily meant ...

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### GCD induction proof

I apologize if this is a duplicate question (believe me, I've searched). This question is a part of an ungraded class warm-up exercise. Question: Using induction, prove that for all positive integers ...
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### Prove $\frac{1\cdot 3\cdot 5\cdots (2n - 1)}{ 2^n(n + 1)!}\cdot 4^n= \frac{1}{n+1} {2n\choose n}$

Prove: $$\frac{1\times 3\times 5\times \cdots \times (2n - 1)}{2^n (n + 1)!} \times 4^n = \frac{1}{n+1} \binom{2n}{n}$$ -Sorry I don't know how to do choose notation in stack exchange. I'm ...
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### Proof that $3^c + 7^c - 2$ by induction

I'm trying to prove the for every $c \in \mathbb{N}$, $3^c + 7^c - 2$ is a multiple of $8$. $\mathbb{N} = \{1,2,3,\ldots\}$ Base case: $c = 1$ $(3^1 + 7^1 - 2) = 8$ Base case is true. Now assume ...
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### For $n \in Z^{\geq 0}$, define $g_n = 2^{2^n} + 1$. Show that $g_0\cdot g_1\cdots g_{n-1} = g_n -2$. [duplicate]

For $n \in Z^{\geq 0}$, define $g_n = 2^{2^n} + 1$. Show that $g_0\cdot g_1\cdots g_{n-1} = g_n -2$ for all $n \in Z^+$. I thought that this could be proved using induction, but then the base case ...
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### Determine the matrix for every n,$\begin{pmatrix}1&1\\1&0\end{pmatrix}^n$.

$\begin{pmatrix}1&1\\1&0\end{pmatrix}^n$ Is the a formula which give us the matrix for every n? I should make a proof with induction.
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### Proof by Induction: "In a Zoo there are$\ k$ monkeys and$\ k$ monkey bars …

I'm struggling hard to prove the following statement/riddle by induction, it is given in the current assignement as a challenge. I really want to understand how to exactly approach such excersises. ...
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### Question about structural induction and predecessor relation

I have two questions, about structural induction and the predecessor relation. Why can't a relation be well-founded if it has an infinite descending chain, provided that it has a maximum element? How ...