This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: HOMEWORK 5 Question 1. Prove by induction that for all n ∈ N,
n i3 =
i=1 n(n + 1) 2 2 . Question 2. Consider the sequence deﬁned recursively by a1 = 2 an+1 = 7an + 9n + 5n Prove by induction that for all n ≥ 1, an = 9n − 5n . 2 Question 3. Consider the sequence deﬁned recursively by a1 = 1 a2 = 3 an+2 = 3an+1 − 2an Prove by induction that for all n ≥ 1, an = 2n − 1. Question 4. Consider the following 4 × 4 square grid from which one square has been removed: 1 2 HOMEWORK 5 Then it is easily checked that it can be covered without overlaps using Lshaped tiles of the following form: Prove that for any n ≥ 1, a 2n × 2n square grid with any one square removed can be covered without overlaps using such Lshaped tiles. ...
View
Full
Document
This note was uploaded on 01/31/2011 for the course MATH 300 taught by Professor Ctw during the Spring '08 term at Rutgers.
 Spring '08
 ctw
 Math

Click to edit the document details