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How do you simplify (2k)!/(2k+2)! to 1/(2(k+1)(2k+1)) ?

Answer 1

Christian Antunez

The expression we want to simplify is

#E = ((2k)!)/((2k+2)!)#.

Since #(2k+2)! = (2k+2)(2k+1)(2k)!#, then:

#E = ((2k)!)/((2k+2)(2k+1)(2k)!)#.

Then:

#E = cancel((2k)!)/((2k+2)(2k+1)cancel(2k)!)#.

This gives

#E = 1/((2k+2)(2k+1))#.

We can rewrite #(2k+2) = 2(k+1)#; then:

#E = 1/(2(k+1)(2k+1))#.

Hope it helped!

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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