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Found: 3

Problems Calculus Number sequences Boundedness, monotonicity Algebra Sequences Recurrent relations Recurrent relations (other)

13–15 3.0

The sequence of numbers \(a_n\) is given by the conditions \(a_1 = 1\), \(a_{n + 1} = a_n + 1/a^2_n\) (\(n \geq 1\)).

Is it true that this sequence is limited?

Problem #PRU-65001

Problems Calculus Number sequences Number sequences (other) Number Theory Divisibility The fundamental theorm of arithmetic. Prime factorisation.

12–14 3.0

In a row there are 20 different natural numbers. The product of every two of them standing next to one another is the square of a natural number. The first number is 42. Prove that at least one of the numbers is greater than 16,000.

Problem #PRU-116589

Problems Number Theory Divisibility Divisibility of a number. General properties Algebra Sequences Recurrent relations Linear recurrent relations Calculus Number sequences Number sequences (other)

13–15 3.0

The sequence of numbers \(a_1, a_2, \dots\) is given by the conditions \(a_1 = 1\), \(a_2 = 143\) and

for all \(n \geq 2\).

Prove that all members of the sequence are integers.