Term independent of x in binomial expansion, (but k is non-integer in expansion?) (1 Viewer)

asd12345 · Apr 18, 2018

Hi I need help with a question as I am getting k as a non-integer when doing the binomial expansion.

Question: Find the term independent of x in the expansion of:
$(\frac{2}{x^4} + x^2)^{14}$

My attempt:

$(\frac{2}{x^4} + x^2)^{14} = \binom{14}{k}(2x^{-4})^{14-k}(x^2)^k$
$= \binom{14}{k}2^{14-k}x^{4k-56}x^{2k}$
$= \binom{14}{k}2^{14-k}x^{6k-56}$
Therefore term independent of x when $6k-56 = 0$

but at this point k = 28/3 and I am not sure how to move forward.

How do I solve this question?

pikachu975 · Apr 18, 2018

That means all the terms have an x in it.

asd12345 · Apr 18, 2018

Thanks, so I guess to answer the question you would say the term independent of x is 0?

HeroWise · Apr 18, 2018

No terms are independet,

Yeah that seems correct

Term independent of x in binomial expansion, (but k is non-integer in expansion?) (1 Viewer)

asd12345

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pikachu975

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asd12345

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HeroWise

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