Binomial Expansion (1 Viewer)

klee98

Member
Joined
Aug 31, 2014
Messages
84
Gender
Male
HSC
2015
I've changed the question!
I know how to do a,b and d
How do you do c?
Any help is greatly appreciated

 

Attachments

Last edited:

InteGrand

Well-Known Member
Joined
Dec 11, 2014
Messages
6,109
Gender
Male
HSC
N/A
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.
 

Users Who Are Viewing This Thread (Users: 0, Guests: 1)

Top