Question

)Show that n2

-1 is divisible by 8,if n is an odd positive integer.
Its urgent.....
Plz be sure for your...answer..​

Answer 1

Answer:

Hence Proved

Step-by-step explanation:

If n is an odd positive integer then it can be written in the form :-

  2m+1   , where m is a natural number .

Now by substituting N by 2m+1 we get

4m^2 + 4m + 1 - 1

4m( m + 1 )

Now on dividing 4m( m + 1 ) by 8 we get :-

$\frac{m(m+1) }{2}$        -    (  i  )

We know that m is a natural number therefore   ( i ) has to be divisible by 2

Hence we proved n^2 -1 is divisible by 8 for n being odd positive integer.

Hope this helped you,