The general term in the expansion of (x+\dfrac{2}{x^2})^{10} is T_{k+1}=\binom{10}{k}x^{10-k}\left(\dfrac{2}{x^2}\right)^k. For which value of k is the term independent of x?

AM-1291

General term of a binomial expansion

A Math · Secondary 4 · Medium · General term of a binomial expansion

The general term in the expansion of

(x+\dfrac{2}{x^2})^{10}

T_{k+1}=\binom{10}{k}x^{10-k}\left(\dfrac{2}{x^2}\right)^k

. For which value of

k

is the term independent of

x

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