Induction Questions (1 Viewer)

[dwarven]

hey all
if you have any induction questions can you upload them to the net plz?

will be appriciated =]

 

[Slidey]

Last time I saw that question was 3 years ago and I still hate it.

 

[vds700]

hey all
if you have any induction questions can you upload them to the net plz?

will be appriciated =]

3 unit HSC Q's by topic, bottom of the Extension 1 resources page

 

[dwarven]

prove, using mathematical induction, that the total number of diagonals in an n-sided polygon is given by n(n - 3)/2

lol
no idea

3 unit HSC Q's by topic, bottom of the Extension 1 resources page

thnx =]

 

[lolokay]

prove, using mathematical induction, that the total number of diagonals in an n-sided polygon is given by n(n - 3)/2

Spoiler

a triangle has 0 diagonals, so it's true for n = 3
with the addition of an extra vertex to the polygon, you can make n-2 diagonals from it (every previous point except adjacent ones) plus 1 extra being made by the 2 points adjacent to it - so a total of n - 1 new diagonals

[n(n-3) + 2n - 2]/2
= [n^2 - n - 2]/2
= (n+1)(n+1-3)/2

so if it is true for n it is true for n+1, and it is true for n=3 so it is true for all polygons

 

[Trebla]

Try this...

 

[dwarven]

Try this...

thnxx

 

[shaon0]

Spoiler

a triangle has 0 diagonals, so it's true for n = 3
with the addition of an extra vertex to the polygon, you can make n-2 diagonals from it (every previous point except adjacent ones) plus 1 extra being made by the 2 points adjacent to it - so a total of n - 1 new diagonals

[n(n-3) + 2n - 2]/2
= [n^2 - n - 2]/2
= (n+1)(n+1-3)/2

so if it is true for n it is true for n+1, and it is true for n=3 so it is true for all polygons

Good answer