Please select a subject first
Advertisements
Advertisements
32n+7 is divisible by 8 for all n ∈ N.
Concept: undefined >> undefined
Find the value of the following trigonometric ratio:
Concept: undefined >> undefined
Advertisements
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
A customer forgets a four-digits code for an Automatic Teller Machine (ATM) in a bank. However, he remembers that this code consists of digits 3, 5, 6 and 9. Find the largest possible number of trials necessary to obtain the correct code.
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
In how many ways can three jobs I, II and III be assigned to three persons A, B and C if one person is assigned only one job and all are capable of doing each job?
Concept: undefined >> undefined
How many natural numbers not exceeding 4321 can be formed with the digits 1, 2, 3 and 4, if the digits can repeat?
Concept: undefined >> undefined
How many numbers of six digits can be formed from the digits 0, 1, 3, 5, 7 and 9 when no digit is repeated? How many of them are divisible by 10 ?
Concept: undefined >> undefined
