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52n −1 is divisible by 24 for all n ∈ N.
Concept: undefined >> undefined
32n+7 is divisible by 8 for all n ∈ N.
Concept: undefined >> undefined
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Find the value of the following trigonometric ratio:
Concept: undefined >> undefined
Find the value of the following trigonometric ratio:
sin 17π
Concept: undefined >> undefined
Find the value of the following trigonometric ratio:
\[\tan\frac{11\pi}{6}\]
Concept: undefined >> undefined
Find the value of the following trigonometric ratio:
Concept: undefined >> undefined
Find the value of the following trigonometric ratio:
\[\tan \frac{7\pi}{4}\]
Concept: undefined >> undefined
52n+2 −24n −25 is divisible by 576 for all n ∈ N.
Concept: undefined >> undefined
32n+2 −8n − 9 is divisible by 8 for all n ∈ N.
Concept: undefined >> undefined
(ab)n = anbn for all n ∈ N.
Concept: undefined >> undefined
n(n + 1) (n + 5) is a multiple of 3 for all n ∈ N.
Concept: undefined >> undefined
72n + 23n−3. 3n−1 is divisible by 25 for all n ∈ N.
Concept: undefined >> undefined
2.7n + 3.5n − 5 is divisible by 24 for all n ∈ N.
Concept: undefined >> undefined
11n+2 + 122n+1 is divisible by 133 for all n ∈ N.
Concept: undefined >> undefined
Given \[a_1 = \frac{1}{2}\left( a_0 + \frac{A}{a_0} \right), a_2 = \frac{1}{2}\left( a_1 + \frac{A}{a_1} \right) \text{ and } a_{n + 1} = \frac{1}{2}\left( a_n + \frac{A}{a_n} \right)\] for n ≥ 2, where a > 0, A > 0.
Prove that \[\frac{a_n - \sqrt{A}}{a_n + \sqrt{A}} = \left( \frac{a_1 - \sqrt{A}}{a_1 + \sqrt{A}} \right) 2^{n - 1}\]
Concept: undefined >> undefined
Prove that n3 - 7n + 3 is divisible by 3 for all n \[\in\] N .
Concept: undefined >> undefined
Prove that 1 + 2 + 22 + ... + 2n = 2n+1 - 1 for all n \[\in\] N .
Concept: undefined >> undefined
7 + 77 + 777 + ... + 777 \[{. . . . . . . . . . .}_{n - \text{ digits } } 7 = \frac{7}{81}( {10}^{n + 1} - 9n - 10)\]
Concept: undefined >> undefined
Concept: undefined >> undefined
Concept: undefined >> undefined
