MYTUTOR SUBJECT ANSWERS

202 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...

5 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

328 SUBJECT SPECIALISTS

£18 /hr

Robert L.

Degree: Geophysics (Masters) - University College London University

Subjects offered: Maths, Physics+ 1 more

Maths
Physics
Geography

“Hi, my name is Robert and I'm studying Geophysics at University College London, currently in my second year, with an interest in hazard and disaster reduction. Having been tutored myself in the past I know the importance of an underst...”

MyTutor guarantee

£18 /hr

Harry B.

Degree: Music (Bachelors) - Cambridge University

Subjects offered: Maths, Russian+ 5 more

Maths
Russian
Music
Latin
History
English Literature
English Language

“Hi there, my name is Harry and I'm a finalist reading music at the University of Cambridge. I absolutely love all types of muisc and fortuantely, in my degree, I'm studying a really wide variety of subjects, ranging from the 13th Cent...”

MyTutor guarantee

£20 /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 3 years and have gathered many different ways of teaching concepts to students in a way that is easily-digestible and understandable. I like to focus on the core understanding of a subject matter and then a...”

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

How do signs change in an inequality?

Find the possible values of x when x^2+8x+15=0

Solve this equation; 5x - 4 = 3x + 7

Solve equations 2x+y=9 and x+2y=6 to find x and y.

View GCSE Maths tutors

Cookies:

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

mtw:mercury1:status:ok