# Recent questions tagged induction

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Calculate, by using an appropriate formula: $$3-1+\frac{1}{3}-\ldots \ldots \ldots \ldots \ldots+\frac{1}{243}$$
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Given a finite sequence $$x_{1,1}, x_{2,1}, \ldots, x_{n, 1}$$ of integers ( $$n \geq 2$$ ), not all equal, define the sequences $$x_{1, k}, \ldots, x_{n, k}$$ by$x_{i, ... 267 views 0 answers The Fibonacci sequence is defined by $$f_1=0, f_2=1$$, and $$f_{n+2}=f_{n+1}+f_n$$ for $$n \geq 1$$. Prove that there is a strictly increasing arithmetic progression whos... 331 views 0 answers Define a sequence $$a_{1}, a_{2}, \ldots$$ by $$a_{1}=\frac{5}{2}$$ and $$a_{n+1}=a_{n}^{2}-2$$ for $$n \geq 1$$. Give an explicit formula for $$a_{n}$$ and prove it. 462 views 1 answers We can also use induction in a definition. For example, the Fibonacci numbers is a sequence of numbers $$F_{0}, F_{1}, F_{2}, \ldots$$ defined by $$F_{0}=F_{1}=1$$ and\[F... 435 views 1 answers What is the induction principle in mathematics? 260 views 1 answers Let $$a_{0}=6$$ and\[a_{n}=\frac{a_{n-1}}{1+a_{n-1}}$for all $$n \geq 1$$. Find $$a_{100}$$.
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Let $$E$$ be an open set in $$R^{n}$$. The classes $$\mathcal{C}^{\prime}(E)$$ and $$\mathcal{C}^{\prime \prime}(E)$$ are defined in the text. By induction $$\mathcal{C}^... 1.2k views 1 answers Prove by Induction :Prove \(3^{n}>2^{n}$$ for all natural numbers $$n$$.
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Let $$S_{N}:=1+\frac{1}{2}+\cdots+\frac{1}{N}$$. Find an estimate for $$N$$ so that $$S_{N}>100$$.
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Prove by induction that for every natural number $n$, $n^{3}+2 n$ is divisible by 3
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An electroscope charged WITHOUT contacting a charged body is charged by:w) inductionx) conductiony) convectionz) insulation
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Show that $s_{n} \leq 2$ for all $n .$ (Hint: Use induction)
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Let $s_{1}=\sqrt{2}$ and $s_{n+1}=\sqrt{2+s_{n}}$ for $n=1,2,3, \cdots$.(i) Show that $\left\{s_{n}\right\}$ is an monotonically increasing sequence. (Hint: Use induction...
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What does electromagnetic induction depend on?
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What is electromagnetic induction in physics?
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Solve for $x$ in the equation $\left(2\sqrt{x}\right)^{n}\left(\dfrac{-1}{\sqrt{x}}\right) = -16$
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Define a sequence of real numbers by the rules\begin{equation*}s_0 = 0 \quad \text{and} \quad s_{n + 1} = \sqrt{3 + s_n} \enspace \text{for } n \geq 0\end{equation*}Show ...
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Consider the Fibonnaci sequence, given by F(0) = F(1) = 1, and for $n \geq 0$, F(n + 2) = F(n) + F(n + 1). Let $r = (\sqrt{5} + 1)/2$. Prove by induction that\begin{equat...
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Prove by induction that\begin{equation*}\sum_{i=1}^{n} i^3 = \left(\sum_{i=1}^{n} i\right)^2.\end{equation*}
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What is False Proof of Induction?
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What is the Generalized Principle of Induction?
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State Faraday’s Law of electromagnetic induction
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A material having uniform magnetization $M$ is in the form of a thin disk with radius $a$ and thickness $h \leq a$. $\overrightarrow{\rm M}$ points along the axis of th...