Find the middle term in the expansion of (1 – 2x + x2)n

Question

Find the middle term in the expansion of (1 – 2x + x²)ⁿ

Asked by Aaryan | 1 year ago | 179

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Accepted Answer

We have,

(1 – 2x + x²)ⁿ = (1 – x)²ⁿ where, n is an even number.

So the middle term is (\( \dfrac{2n}{2}\) + 1) = (n + 1)^th term.

Now,

T_n = T_n+1

= ²ⁿC_n (-1)ⁿ (x)ⁿ

= \( \dfrac{(2n)!}{(n!)^2} (-1)^n x^n\)

Hence, the middle term is \( \dfrac{(2n)!}{(n!)^2} (-1)^n x^n\)

Answered by Sakshi | 1 year ago