in Combinatory edited by
121 views
0 votes
0 votes

Let $\{a_{n}\}$ be a sequence of real numbers. The backward differences of this sequence are defined recursively as shown next. The first difference $\triangledown a_{n}$ is

$$\triangledown a_{n} = a_{n} − a_{n−1}.$$

The $(k + 1)^{\text{st}}$ difference $\triangledown^{k+1}a_{n}$ is obtained from $\triangledown ^{k} a_{n}$ by

$$\triangledown ^{k+1}a_{n} = \triangledown^{k}a_{n} − \triangledown ^{k}a_{n−1}.$$

Find $\triangledown^{2} a_{n}$ for the sequence $\{a_{n}\},$ where

  1. $a_{n} = 4.$
  2. $a_{n} = 2n.$
  3. $a_{n} = n^{2}.$
  4. $a_{n} = 2^{n}.$
in Combinatory edited by
by
121 views

Please log in or register to answer this question.

Related questions

Quick search syntax
tags tag:apple
author user:martin
title title:apple
content content:apple
exclude -tag:apple
force match +apple
views views:100
score score:10
answers answers:2
is accepted isaccepted:true
is closed isclosed:true