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  4. The binomial expansion of ( x k +(1/ x 2 k ))3 n , n ∈ N contains a term independent of x

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Q. The binomial expansion of $\left( x ^{ k }+\frac{1}{ x ^{2 k }}\right)^{3 n }, n \in N$ contains a term independent of $x$

Binomial Theorem

Solution:

$T _{ r +1}={ }^{3 n } C _{ r } x ^{3 nk -3 rk } \Rightarrow D$ where $r = n$