Assignment - Homework 5

Assignment- - 2 n 2 2 regions if no two lines are parallel and no three lines intersect in a common point 5 Let F(0 = 0,F(1 = 1 and F n = F n-1 F

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
MA2312 Homework 5 John Iacono February 24, 2010 1. Prove by induction, that for all integer n where n > 1 n X i =1 1 i 2 < 2 - 1 n 2. Prove by induction, that for all integer n where n 1 n X i =1 i ( i + 1)( i + 2) = n ( n + 1)( n + 2)( n + 3) 4 3. Prove by induction, that for all integer n where n 1 n X i =1 i i Y j =1 j = n +1 Y i =1 i - 1 4. Prove by induction, that n lines separate the plane into ( n
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 2 + n + 2) / 2 regions if no two lines are parallel and no three lines intersect in a common point. 5. Let F (0) = 0 ,F (1) = 1 and F ( n ) = F ( n-1) + F ( n-2) ,n ≥ 2. Prove there is some c that by induction for all integer n > c , 1 . 5 n < F ( n ) < 2 n < n ! < n n 1...
View Full Document

This note was uploaded on 03/07/2010 for the course MA 2312 taught by Professor Johniacono during the Spring '10 term at NYU Poly.

Ask a homework question - tutors are online