Mathemaatical Inducction (1 Viewer)

math man

Member
Joined
Sep 19, 2009
Messages
503
Location
Sydney
Gender
Male
HSC
N/A
I'm on my iPhone ATM, but question 3 should be
Done using sum of rectangles under curve and using
The bigger and lower rectangles to bound it. I'll show
You later if someone else doesn't
But if you had to do it using induction it is easiest
to separate the inequality and do induction twice
and then conclude that inequality
 
Last edited:

zeebobDD

Member
Joined
Oct 23, 2011
Messages
414
Gender
Male
HSC
2012
hmm was thinking about splitting the inequality, il try that:)
 

deswa1

Well-Known Member
Joined
Jul 12, 2011
Messages
2,256
Gender
Male
HSC
2012
If you split the inequality, it isn't that hard. If you still can't do it, I can post my solution, but have a go first :)
 

deterministic

Member
Joined
Jul 23, 2010
Messages
423
Gender
Male
HSC
2009
Consider each part of the inequality separately. When we add to all parts of inequality, the left part of the inequality becomes:

Where the third line is due to the fact for

The right hand part of inequality becomes:


It follows that:
 

Trebla

Administrator
Administrator
Joined
Feb 16, 2005
Messages
8,110
Gender
Male
HSC
2006
I'll go straight to the inductive proof step for the LHS of the inequality

First we establish a result as follows



Now to the induction step



Hence we can claim that



However, the result holds for n = 1 as an equality and so subsequent integers of n will lead to strict inequality, hence the result as a weak inequality is true by induction i.e.

 
Last edited:

Users Who Are Viewing This Thread (Users: 0, Guests: 1)

Top