Forum - Algebra

Newton binomial

Mary
Visitor
2016-06-27 06:08:28
#1
Hi,
I need help with Newtons' binomial. If we developing the binomial left ( xsqrt[4]{x}+frac{1}{sqrt{x}} right )^{n} the sum of rank 2k coefficients is 128. Which is the term which contains x3?

 

RE: Newton binomial

Mary
Visitor
2016-06-27 06:11:16
#2
ooofff!!!!
this is a problem with equations editor in this forum:
the binomial is
Newtons Binomial

RE: Newton binomial general term

TeacherM
Visitor
2016-06-27 06:39:28
#3
We have the sum of even coefficients:
Newton binolmial coefficients mathbf{C}_{n}^{0}+mathbf{C}_{n}^{2}+mathbf{C}_{n}^{4}+mathbf{C}_{n}^{6}+...=2^{n-1}=128 => n=8
And the formula in general term (in Newtons' binomial) is:
T_{k+1}=mathbf{C}_{8}^{k}cdot (xsqrt[4]{x})^{8-k}cdot left ( frac{1}{sqrt{x}} right )^{k}=mathbf{C}_{8}^{k}(x^{frac{5}{4}})^{8-k}x^{frac{-k}{2}}=mathbf{C}_{8}^{k}xfrac{40-7k}{4}
so though, frac{40-7k}{4}=3=>k=4



That's means that the term k+1 = 5,i.e. fifth term which contains   x3

 
 

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