Prove that x^n > (x - 1)^n + (x - 2)^n
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Prove that x^n > (x - 1)^n + (x - 2)^n

[From: ] [author: ] [Date: 11-06-28] [Hit: ]
x=3.which is obviously false.So the assumption must be false. But the assumption is the statement, so the statement is false.What did you mean to say?......
x > 0; n integer

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Sounds like induction to me :P

Let n=1.
Then x-1 + x-2 = 2x-3. x>0, so…

um...


Your statement is false.

Assume it is true.
Then it should be true for n=1, x=3.

But
3^1 > (3-1)^1 + (3-2)^1
3 > 2 + 1

which is obviously false.
So the assumption must be false. But the assumption is the statement, so the statement is false.

What did you mean to say?

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x^n > (x +1)^N + (x+2)^n
Prove true for a number
(2)^1> (2-1)^1 + (2-2)^1
2>1
therefore statement is true for 1

Assume true for x^k therefore
x^k > (x-1)^k + (x-2)^k

Prove true for k+1
x^k+1 > (x-1)^k+1 +(x-2)^k+1
LHS (X-1)k+1 + (x-2)^k+1
multiply brackets and get quadratic and solutions you would see that the statement is true
1
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