This preview shows page 1. Sign up to view the full content.
Unformatted text preview: , 1001117 ,... are divisible by 53. Hint: use induction, consider the dierence between the consecutive numbers. 10. Find the compact formula for the sum 1 1! + 2 2! + 3 3! + + n n ! . Hint: guess a formula for n = 1 , 2 , 3, then prove it by induction. 11. Prove that the remainder of 3 n modulo 20 is less than 10 for all n . 12. Prove that the number (2 k )! /k ! is divisible by 2 k and not divisible by 2 k +1 . Hint: use induction. 13. Prove the following identity for the Fibonacci numbers: F 1 + F 2 + ... + F n = F n +21 . Hint: use induction. 1...
View
Full
Document
This note was uploaded on 01/25/2012 for the course MAT 312 taught by Professor Bescher during the Summer '08 term at SUNY Stony Brook.
 Summer '08
 BESCHER
 Algebra, Equations, Remainder

Click to edit the document details