MYTUTOR SUBJECT ANSWERS

858 views

Prove that the difference of any two consecutive square numbers is odd

It is important we first define what we mean by an odd and even number.
An even number is any integer (whole number) number divisible by 2 so we can express any even number as 2x where x is any integer. When counting, every even number is followed by an odd number; 1,2,3... etc.
We can then express any odd number as 2x+1 as it will just be the next number after 2x i.e. add one.
Now any square number can be expressed as n^2 where n is any integer. The next square number can also be written as (n+1)^2 since it will be the square of the next number after n i.e. n+1.
As such, the difference of any two consecutive square numbers can be written as (n+1)^2 - n^2   
Expanding this we get (n^2 + 2n + 1) - n^2
This reduces to 2n+1 since the n^2 values cancel.
Since any odd number can be written in the form 2x+1  where x is any integer as earlier defined, 2n+1 is an odd number for any value of n which completes the proof.  

Amar H. 13 plus  Maths tutor, A Level Maths tutor, 11 Plus Maths tuto...

10 months ago

Answered by Amar, who has applied to tutor GCSE Maths with MyTutor


Still stuck? Get one-to-one help from a personally interviewed subject specialist

448 SUBJECT SPECIALISTS

£22 /hr

Pooja D.

Degree: Medicine (Bachelors) - Birmingham University

Subjects offered:Maths, Science+ 6 more

Maths
Science
Physics
Chemistry
Biology
.UKCAT.
-Personal Statements-
-Medical School Preparation-

“I have tutored for the past 4 years and have gathered many ways of teaching concepts to students in a way that is easily-digestible and understandable. ”

£20 /hr

Max G.

Degree: Mathematics and Physics (Masters) - Durham University

Subjects offered:Maths, Physics+ 2 more

Maths
Physics
Chemistry
Biology

“I am a maths and physics student at the University of Durham, for as long as I can remember i have been obsessed with all things science! I am patient, friendly and most of all understanding to the fact that the sciences aren't for ev...”

£18 /hr

Tabitha M.

Degree: Modern Languages (Bachelors) - Newcastle University

Subjects offered:Maths, Spanish

Maths
Spanish

“Hi!I am a first year student at the University of Newcastle studying Spanish and Japanese. I am patient, reliable and looking forward to hearing from you!”

About the author

£18 /hr

Amar H.

Degree: Mathematics (Bachelors) - Manchester University

Subjects offered:Maths, Physics+ 2 more

Maths
Physics
Further Mathematics
-Personal Statements-

“About Me: Hi, my name is Amar and I'm currently reading Maths at the University of Manchester. I have a real passion for the subject and love teaching it to others and hope my students will love it as much as I do.  Having being tutor...”

MyTutor guarantee

You may also like...

Other GCSE Maths questions

why does 4 / 0.5 =8?

There are 200 students in Year 10 110 are boys. There are 250 students in Year 11 140 are boys. Which year has the greater proportion of boys? (Taken from Nov 2014 AQA Unit 2)

What is the best way to revise for my Maths GCSE?

Solve the equation ((2x+3)/(x-4))-((2x-8)/(2x+1))=1

View GCSE Maths tutors

We use cookies to improve your site experience. By continuing to use this website, we'll assume that you're OK with this. Dismiss

mtw:mercury1:status:ok