Binomials (1 Viewer)

[Kutay]

Hey i have noticed that most of the questions 7 have a hard binomial and i just dont understand them, and would just like to get maybe the first 2 marks out?
anyone got some tips besides practice like , are there any formulas that if mention will get marks, cause i think its too late to learn the diff and integrating binomials

 

[KFunk]

Well, two things to look for are the following. If you see numbers out front in a question like:

1) Find the value of ⁿC₁ + 2ⁿC₂ + 3ⁿC₃ + ... + nⁿC_n then it's a safe bet that the question involves differentiating and subbing in x=1. In this case if would be:

1 + ⁿC₁x + ⁿC₂x² +...+ ⁿC_nxⁿ = (1 + x)ⁿ then differentiate both sides.

ⁿC₁ + 2ⁿC₂x + 3ⁿC₃x² + ... + nⁿC_nx^n-1 = n(1+x)^n-1

As you can see you have the same pattern on the left hand side. You can get the one I first mentioned by subbing in x=1. If you ever see this pattern of r.ⁿC_r then you can expect differentiation to be involved.

2) On the other hand if you have something like:

1 + (1/2)ⁿC₁ + (1/3)ⁿC₂ +...+ (1/(n+1))ⁿC_n

Then you can expect integration to be involved. I've had enough typing so maybe someone else would like to go through the process of an integration one? Anyhow, I hope that gives you a couple of things to look for.