Number Sequences1
... In the sequence 2, 4, 6, 8, 10... there is an obvious pattern. Such sequences can be expressed in terms of the nth term of the sequence. In this case, the nth term = 2n. To find the 1st term, put n = 1 into the formula, to find the 4th term, replace the n's by 4's: 4th term = 2 × 4 ...
... In the sequence 2, 4, 6, 8, 10... there is an obvious pattern. Such sequences can be expressed in terms of the nth term of the sequence. In this case, the nth term = 2n. To find the 1st term, put n = 1 into the formula, to find the 4th term, replace the n's by 4's: 4th term = 2 × 4 ...
university of maryland mathematics competition
... 1. Four positive numbers are placed at the vertices of a rectangle. Each number is at least as large as the average of the two numbers at the adjacent vertices. Prove that all four numbers are equal. 2. The sum 498 + 499 + 500 + 501 = 1998 is one way of expressing 1998 as a sum of consecutive positi ...
... 1. Four positive numbers are placed at the vertices of a rectangle. Each number is at least as large as the average of the two numbers at the adjacent vertices. Prove that all four numbers are equal. 2. The sum 498 + 499 + 500 + 501 = 1998 is one way of expressing 1998 as a sum of consecutive positi ...
`A` List Problems
... axioms for set theory. We will take the integers, Z, the subset N of natural numbers (that is, the positive integers), and their properties as given. The goal of this problem is, using the integers and their properties, to construct the set Q, define the operations of ‘addition’ and ‘multiplication’ ...
... axioms for set theory. We will take the integers, Z, the subset N of natural numbers (that is, the positive integers), and their properties as given. The goal of this problem is, using the integers and their properties, to construct the set Q, define the operations of ‘addition’ and ‘multiplication’ ...
infinite series
... We are not going to spend much time on theory of sequences because sequence is just a function, so we can apply all the limit theory we learned in Calculus 1 ...
... We are not going to spend much time on theory of sequences because sequence is just a function, so we can apply all the limit theory we learned in Calculus 1 ...
