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2017-12-21, 12:03   #6
Nick

Dec 2012
The Netherlands

22·353 Posts

Quote:
 Originally Posted by MushNine (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.