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1.6.3 Binomial expansion for rational n (A-level only)

When does the expansion of (1+x)n(1+x)^n(1+x)n terminate?

A

It terminates when nnn is a non-negative integer.

B

The first terms are (1+x)n=1+ (1+x)^n=1+\,(1+x)n=1+nxnxnx+ +\,+n(n−1)2!x2\frac{n(n-1)}{2!}x^22!n(n−1)​x2+ +\,+n(n−1)(n−2)3!x3\boxed{\frac{n(n-1)(n-2)}{3!}x^3}3!n(n−1)(n−2)​x3​+⋯+\cdots+⋯.

C

The powers of uuu decrease more rapidly.

D

The first terms are (1+x)n=1+ (1+x)^n=1+\,(1+x)n=1+nxnxnx+ +\,+n(n−1)2!x2\boxed{\frac{n(n-1)}{2!}x^2}2!n(n−1)​x2​+ +\,+n(n−1)(n−2)3!x3\frac{n(n-1)(n-2)}{3!}x^33!n(n−1)(n−2)​x3+⋯+\cdots+⋯.

1.6.3 Binomial expansion for rational n (A-level only) Flashcards

  1. A Level
  2. /Maths
  3. /1.6.3 Binomial expansion for rational n (A-level only)

Flashcards for OCR (MEI) A Level Maths 1.6.3 Binomial expansion for rational n (A-level only), covering the key formulae, methods and definitions you need to recall for Component 01, Component 02 and Component 03. 20 cards, matched to the OCR (MEI) A Level Maths (H640) specification. Recall questions account for roughly 50% of marks at A Level Maths, so these target the marks you can secure before the paper starts.

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