tony700
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Proving an equality using induction proof not working
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pizzasky
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Our inductive hypothesis is ##\prod\limits_{n=1}^{k}n(2k+2-2n)=2^k(k!)^2##, for some ##k\in\{1,2,...\}##.
We want to show that ##\prod\limits_{n=1}^{k+1}n(2(k+1)+2-2n)=2^{k+1}((k+1)!)^2##.
We want to show that ##\prod\limits_{n=1}^{k+1}n(2(k+1)+2-2n)=2^{k+1}((k+1)!)^2##.
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tony700 said:
That's what you're to prove.
I think it's clearer if you do the induction step as follows.
Assume that ##\displaystyle \ \prod_{n=1}^{k}n(2k+2-2n)=2^k(k!)^2 \ ## is true for ##\ k=m\ ## for some ##m>0##. Then show that it's true for ##k = m+1##. You must replace every ##k## with ##m## or ##m+1## as appropriate.
Note: In the jpeg image that you showed, you needed to have extra parentheses in a number of places.
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Are you absolutely required to use induction? If not, just writing out the product directly and simplifying is by far the easiest way to do the problem.tony700 said: