1.

N3 + (n + 1)3 + (n + 2)3 is always divisible by​

Answer»

Answer is nine (9).

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Class 12

MATHS

PRINCIPLE OF MATHEMATICAL

Shwo that

is divisible 9 for everynatural NUMBER n.

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Text Solution

Solution

Let

is divisible by 9.
When


=1+8+27
=36, which is divisible by 9.

is true.

is divisible by 9. (i)
To prove P(k+1) is true i.e.

is divisible by 9.




which is divisible by 9.
HENCE P(k+1) is true, WHENEVER P(k) is true.
From (a) and (b), it follows that P(n) is true for all natural number.


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