Question

if n is odd (11) n+1 is divisible by' !​

Answer 1

Answer:

If n is odd 11 then n+1 is divisible by 2,3,4,6,12

Hope it helps u.....

Answer 2

Answer:

We know ,

odd number in the form of (2Q +1) where Q is a natural number ,

so, $n² -1 = (2Q + 1)² -1$

$= 4Q² + 4Q + 1 -1$

$= 4Q² + 4Q$

now , checking :

$Q = 1$ then,

$4Q² + 4Q = 4(1)² + 4(1) = 4 + 4 = 8$ , it is divisible by 8.

$Q =2$ then,

$4Q² + 4Q = 4(2)² + 4(2) =16 + 8 = 24$, it is also divisible by 8 .

$Q =3$ then,

$4Q² + 4Q = 4(3)² + 4(3) = 36 + 12 = 48$ , divisible by 8

It is concluded that $4Q² + 4Q$ is divisible by 8 for all natural numbers.

Hence, n² -1 is divisible by 8 for all odd value of n .

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