Very short proof that limit preserving functions (continuous functions) on complete partial orders are necessarily monotone.
Posts Tagged ‘ analysis ’
Let , where k is an integer. Prove that for any positive integer n the number
is divisible by .
Define the sequence recursively by and
Find an explicit formula for in terms of n.
Let be defined by the recurrence relation , with . Show that the expression depends only on b and , but not on a.
Find the general term of the sequence given by , and
Let . Show that for any positive integers there exists unique numbers such that the polynomial is divisible by p(x)
We derive Binet’s equation for the nth Fibonacci number as
We derive a general technique for solving full rank linear recursive sequences. Formally, a kth linear recursive sequence is defined as
Consider the sequences , defined recursively by