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When does the expansion of (1+x)n(1+x)^n(1+x)n terminate?
It terminates when nnn is a non-negative integer.
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+⋯.
The powers of uuu decrease more rapidly.
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+⋯.
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1.6.3 Binomial expansion for rational n (A-level only) Flashcards
20 flashcards on OCR (MEI) A Level Maths 1.6.3 Binomial expansion for rational n (A-level only): the key formulae, methods and definitions you need to recall for Component 01, Component 02 and Component 03.