Question

A square number can be expressed as product of consecutive even / odd numbers. For $n^2$, it is represented as:

• A. $(n-1)(n+1)=n^2-1$
• B. $(n+1)(n+1)=n^2+1$
• C. $(n-1)(n-1)=n^2-1$
• D. $(n^2-1)(n^2+1)=n^2-1$

Answer 1

The correct option is A $(n-1)(n+1)=n^2-1$

The product of any consecutive even or odd numbers can be expressed as a square number.

Let's take two consecutive odd number 3 and 5.
$3\times 5=15=16-1$
$3\times 5=4^2-1$
$(4-1)(4+1)=4^2-1$

The genaralised formula can be written as:
$(n-1)(n+1)=n^2-1$