Binomial Expansion (1 Viewer)

klee98

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I've changed the question!
I know how to do a,b and d
How do you do c?
Any help is greatly appreciated

 

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InteGrand

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I've changed the question!
I know how to do a,b and d
How do you do c?
Any help is greatly appreciated

If you evaluate the partial sums from part (b), you'll see that the guess to use is .

I'll only show the induction step. (I assume you can easily do the base case step, assuming you know how to do mathematical induction proofs.)

Assuming , we show .
.

, where is the nth term of the series in the question (this is the typical way to do summation induction proofs)

, by the inductive hypothesis and the fact that (given)

(using factorial rules to take a common denominator, the rule being (n+1)! = (n+1).n!)

(expanding the numerator)

(simplifying the numerator), which is what we wanted to show.
 

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