General Binomial Expansion (AQA A-Level Mathematics): Flashcards

📚Flashcards
General Binomial Expansion
Sign up to keep revising.Create a free account to study more flashcards and track your progress.

Practise the cards

10 cards from this deck

Show

Formula for (nr)\binom{n}{r}

n!r!(nr)!\frac{n!}{r!(n-r)!}

Validity condition for general (1+x)n(1+x)^n expansion

x<1|x| < 1 and nRn \in \mathbb{R}

First 3 terms of (1+x)n(1+x)^n expansion

1+nx+n(n1)2!x21 + nx + \frac{n(n-1)}{2!}x^2

Can (1+x)n(1+x)^n expand if nn not a positive integer?

Yes, if x<1|x| < 1

Value of (496)\binom{49}{6} (lottery jackpot)

13,983,81613,983,816

Coefficient of x6x^6 in (2+x)12(2+x)^{12}

59,13659,136

Approximation of 1.0461.04^6 using binomial expansion

1.2641.264

(1+2x)1(1+2x)^{-1} expanded up to and including x2x^2 term

12x+4x21 - 2x + 4x^2

Coefficient of x8x^8 in (1+2x2)6(1+2x^2)^6

240240

Constant term in (x+1x)4(x + \frac{1}{x})^4

66

Join 100,000+ A-Level students studying Flashcards with us.

Select your subjects, and get access to A+ resources today.