Binomials

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9 07, 2017

Finding Coefficients

By |2017-07-09T17:03:48+10:00July 9th, 2017|Tags: , , |0 Comments

Finding Coefficients $${}^n{C_r}{(a)^{n - r}}{(b)^r} = A{x^c}$$   worked examples Find the coefficient of x4 in the expansion of  $${\left( {x - \frac{2}{x}} \right)^{12}}$$. 12Ck x12 – k (2/x)k = Ax4 using the formula $${}^n{C_r}{(a)^{n - r}}{(b)^r} = A{x^c}$$ where n = 12, a =  x, b = [...]

9 07, 2017

Independent Term

By |2017-07-09T09:47:57+10:00July 9th, 2017|Tags: , , |0 Comments

Independent Term $${}^n{C_r}{(a)^{n - r}}{(b)^r} = A{x^0}$$   worked examples Find the term that is independent of x in the expansion of $${\left( {\frac{1}{{{x^3}}} + 2{x^5}} \right)^{16}}$$.   $${}^{16}{C_k}{\left( {\frac{1}{{{x^3}}}} \right)^{16 - k}}{(2{x^5})^k} = A{x^0}$$   using the formula $${}^n{C_r}{(a)^{n - r}}{(b)^r} = A{x^0}$$ where n = 16, a [...]

18 08, 2015

Coefficient Relationships

By |2018-02-11T12:19:49+10:00August 18th, 2015|Tags: , , |0 Comments

Coefficient Relationships worked examples The coefficients of x10 and x5 are equal in the expansion of (1 + x)n. Find the value of n.   consider the terms nC8x8 and nC7x7 and look only at their coefficients $$\frac{n!}{8!(n-8)!}=\frac{n!}{7!(n-7)!}$$ divide both sides by n! $$\frac{1}{8!(n-8)!}=\frac{1}{7!(n-7)!}$$ reciprocal both sides  8!(n - 8)! = 7!(n [...]

18 08, 2015

Greatest Coefficient

By |2017-07-08T23:20:02+10:00August 18th, 2015|Tags: , , |0 Comments

Greatest Coefficient $$\frac{{{T_{k + 1}}}}{{{T_k}}} > 1$$ $$\frac{n-k+1}{k}.\frac{b}{a}>1$$ worked examples Find the greatest coefficient of (x2 + 2)9.   $$\frac{{{}^9{C_k}{{({x^2})}^{9 - k}}{{(2)}^k}}}{{{}^9{C_{k - 1}}{{({x^2})}^{9 - (k - 1)}}{{(2)}^{k - 1}}}} > 1$$   using the formula $$\frac{{{T_{k + 1}}}}{{{T_k}}} > 1$$ where, nCk = $$\frac{{n!}}{{k!(n - k)!}}$$ Tk + [...]

18 08, 2015

Binomials

By |2017-07-09T17:05:43+10:00August 18th, 2015|Tags: , |0 Comments

Binomials Go to the Binomials Forum to see more questions or ask your own Topics Covered in Binomials Pascal's Triangle Greatest Coefficient Finding Coefficients Independent Term Coefficient Relationships Binomial Expansion Challenging Proofs   Formulas Used in [...]

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