MC-vragen voor 17 plussers (500-600) VARIA

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Dⁿ xⁿ = n! of (xⁿ)⁽ⁿ⁾ = n!	⁰⁷
$f(x)=\frac{x}{1-x}\; \Rightarrow \;\; f^{(n)}(x)=\frac{n\,!}{(1-x)^{n+1}}$	^J3
^{M.Rij met reden q →} $s_{n}=t_{1}\frac{1-q^{n}}{1-q}$	⁰⁹

cos (θ + n ) = (−1)ⁿcos θ	^N5
sin (2ⁿx) = 2ⁿ.sin x.cos x .cos 2x....cos (2ⁿ⁻¹x)	¹⁶
tan 10ⁿ = tan 100 voor n = 2, 3, 4, ...	⁶⁰
A.B = B. A ⇒ A.Bⁿ = Bⁿ. A (matrix)	⁶⁸
$\overline{ \bigcap_{i=1}^{n}\: A_{\, i} } \: =\: \bigcup_{i=1}^{n}\overline{A_{\, i}}$ ^{(deelverzamelingen)}	⁷³
D xⁿ = n.xⁿ⁻¹ (afgeleide)	⁷⁸
(r.cis θ)ⁿ = rⁿ. cis nθ (DE MOIVRE) ℂ	⁸¹
Dⁿ sin x = sin (x + n. )	⁸³
Dⁿ (x.e^x) = (x + n).e^x	^L4
Dⁿ (x².e^x) = [ x² + 2nx + n(n − 1) ].e^x	^L4
$C_{n}^{0}+C_{n}^{1}+C_{n}^{2}+ \cdots C_{n}^{n} = 2^n \quad \forall\: n\in \mathbb{N}$	⁸⁹
$2\cos \frac{\pi }{2^n}=\sqrt{2+\sqrt{2+\sqrt{\cdots }}}\; \, \; _{n-1\; tweetjes\; in\; RL}^{n-1\; wortelvormen}$	⁹⁷
xⁿ − 1 = (x − 1)(xⁿ⁻¹ + xⁿ⁻² + ... + 1)	^T7
$x+x^2+x^3+ \cdots +x^n = \frac{x^{\, n+1}-x}{x-1}$	^A0
$\sum_{i=2}^{n}\; C_{i}^{\, 2}= C_{n+1}^{\;3} \quad (n = 2, 3, ...)$	^Q9
$1.C_{n}^{\, 1}+2.C_{n}^{\, 2}+3.C_{n}^{\, 3}+\cdots + n.C_{n}^{\, n} = n\, .\, 2^{n-1}$	^A3
(1+ sec 2α)(1+ sec 4α)...(1+ sec 2ⁿα ) = tan (2ⁿα).cot α	^A7
$\cos\alpha.\cos2\alpha.\cos 4\alpha.\cdots .\cos\: (2^{n}\alpha )=\frac{\sin\: (2^{n+1}\alpha ) }{2^{n+1}.\sin \alpha }$	^A8
t₁ = 1 ∧ t_n+1 = 3t_n− 1 ⇒ t_n = (3ⁿ⁻¹ + 1)	^B4
t₁ = 1 ∧ t_n = 2.t_n−1 + n ⇒ t_n = 2ⁿ⁺¹ − n − 2	^D4
$https://latex.codecogs.com/png.image?\dpi{110}t_1\!=\!n,\: t_2\!=\!2,\:t_n=t_{n\!-\!1}+(n\!-\!1)t_{n\!-\!2}\Rightarrow t_n\geqslant \sqrt{n!}$	^S2
t₀=-1, t₁=1, t_n= 4, t_n−1− 3.t_n−2 ⇒ t_n = 3ⁿ− 2	^J2
Aantal diagonalen n-hoek is n (n − 3)	^D3
Van rij { t _n} is s_n = 2n − t_n ⇒ t_n = ? (formule)	^F7
$\mathbf{A}=\begin{bmatrix} 1 & x\\ 0 & 1 \end{bmatrix}\; \: \Rightarrow \; \: \mathbf{A}^n= \begin{bmatrix} 1 & nx \\ 0 & 1 \end{bmatrix}$	^G0
$\mathbf{A}=\begin{bmatrix} 1 & x\\ 0 & 1 \end{bmatrix}\; \: \Rightarrow \; \: \mathbf{A}^n= \begin{bmatrix} 1 & nx \\ 0 & 1 \end{bmatrix}$	^R8
$\mathbf{A}=\begin{bmatrix} 2 & 1\\ -1 & 0 \end{bmatrix}\; \Rightarrow \: \: \mathbf{A}^n= \begin{bmatrix} n+\!1 & n \\ -n & 1\!-n \end{bmatrix}$	^R9
$https://latex.codecogs.com/png.image?\dpi{110}\mathbf{A}=\begin{bmatrix} 1 & 1\\ 0 & 2 \end{bmatrix}\; \: \Rightarrow \; \: \mathbf{A}^n= \begin{bmatrix} 1 & 2^n\!-\!1 \\ 0 & 2^n \end{bmatrix}$	^T5
Voor n >13 bestaan x en y zó dat n = 3x+8y (in ℕ)	^G5
1 = som van 3, 4, 5,... verschillende stambreuken	^G6
$\overline{\sum_{k=1}^{n}\: z_k } = \sum_{k=1}^{n} \: \overline{z_k}$ ^{(Complexe getallen)}	^G9
$\sqrt{5+\sqrt{5+\sqrt{5+\cdots \sqrt{5}}}}\: <\: 3$	^E1
$$$\overbrace{4...4}^{n \;\; keer\; 4}$$\! 3 \; \; is\; \mathbf{niet}\; deelbaar\; door\; \; 13$	^A1
$120$$\underbrace{3\, 3\ ..... 3}_{n \; cijfers}08 \;\; \; is \; deelbaar \;door \;19$	^B0
$F_n\: \geqslant \left ( \frac{8}{5} \right )^{n-2} \quad (FIBONACCI)$	^H9
(3 + )ⁿ + (3 − )ⁿ is geheel ∀ n ∈ ℕ	^I2
SP_n = (n − 1).n.(n + 1).(3n+2)	^I7
SPO_n = n(n − 1)(3n²− n − 1)	^I8
t_n ≥ ()ⁿ⁻² ( n = 4,5,...)	^J8
$\sqrt{1+n\sqrt{1+(n\! +\! 1)\sqrt{\cdots }}}\: =\: n+1$	^K1
$https://latex.codecogs.com/png.image?\dpi{110}a + \frac{1}{a}\in \mathbb{Z}\quad\Rightarrow\quad a^n+ \frac {1}{a^n} \in \mathbb{Z}$ ^{(n=1,2, ...)}	^L1
a₁= 3 ∧ a_n = 3 a_n−1 − 2 ⇒ a_n = 2.3ⁿ⁻¹ + 1	^L5
t₁= 3 ∧ t_n+1 = 3 t_n + 4 ⇒ t_n = 5.3ⁿ⁻¹ − 2	^R7
t₀= 3 ∧ t_n+1 = 2 t_n+ 2n − 4 ⇒ t_n = 2ⁿ− 2n + 2	^S3
$\small{\displaystyle\sum_{i=1}^{n}\;i.2^{n-i}=2^{n+1}-(n+2)}$	^L9
som hoeken n-hoek is (n − 2).180°	^N7
$\small \# \, V = n \; \Rightarrow \; \mathbb {P}\, (V)=2^{n} $	^O0
$\frac{3n^2}{2}\!+\!\frac{2n^3}{3}\!-\!\frac{n}{6}\in \mathbb{N}\quad ,\forall n \in \mathbb{N} $	^S7
$\frac{n^5}{5}+\frac{n^3}{3}+\frac{n^2}{2}-\frac{n}{30}\in \mathbb{N}\quad ,\forall n \in \mathbb{N} $	^T8
$\frac{n^7}{7}+\frac{n^5}{5}+\frac{2\,n^3}{3}-\frac{n}{105}\: \in \mathbb{N}\; ,\forall n \in \mathbb{N} $	^T9

V o l l e d i g e i n d u c t i e
Mathematical induction (Engels)
Vollständige Induktion (Duits)
Induction Mathématique (Frans)
Indução matemática (Portugees)
Induzione matematica (Italiaans)
Inducción completa (Spaans)

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