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Old 2017-12-21, 12:03   #6
Nick's Avatar
Dec 2012
The Netherlands

22·353 Posts

Originally Posted by MushNine View Post
(Proving, for A > 0, (A+1)^n -1 = Am)
(m is just some number which satisfies the equation)
Let \(a\) and \(b\) be any numbers.
  1. What is \((a-b)(a+b)\)?
  2. What is \((a-b)(a^2+ab+b^2)\)?
  3. What is \((a-b)(a^3+a^2b+ab^2+b^3)\)?
  4. What is \((a-b)(a^4+a^3b+a^2b^2+ab^3+b^4)\)?
Can you see the pattern?
If you take any integer \(A\) and set \(a=A+1\) and \(b=1\) in the above, it gives your result. So this is a more general version.
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