Hi,
I've only just recently started doing some binomial questions. In a textbook, I got through 8.1 fine, but got stuck on a few 8.2 questions. (The first two questions are from a textbook). Also, I found that I could do some of the past paper questions on binomial theorem, but the last two pics are 2 questions which I didn't how to approach.
Thanks.
Hey there! I'll give you a bit of a hand!
I'm a tad short on time so I'll leave your first question, it has a bit of messy algebra, if no-one has jumped in by this evening I'll come back!
Quite a few of your other questions are very similar, and just require equating coefficients for binomial identities. Let me use the 1996 question as an example. For the result we need to prove, the RHS is the coefficient of x^4 on the right hand side of the result we are given (did you spot this?)
So, let's see what the coefficient of x^4 is on the LHS:
Notice that we need pairs of term that give a total power of x^4, yielding:
I think you see where I'm heading, it gives the LHS of the result, and we are done!
Many questions require this method of thinking, it is what is required in your second textbook question.
Oops, gotta go (train), however, for your 1992 question:
i) x=-1 might work
ii) Hmmm, I wonder what integrating the given expression might do...