Find the middle term in the expansion of (2/3x – 3/2x)20

Question

Find the middle term in the expansion of \( (\dfrac{2}{3x} – \dfrac{3}{2x})^{20}\)

Asked by Sakshi | 1 year ago | 65

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Accepted Answer

where, n = 20 (even number)

So the middle term is (\( \dfrac{n}{2}\) + 1)

= (\( \dfrac{20}{2}\) + 1) = (10 + 1) = 11. ie., 11^th term

Now,

T₁₁ = T₁₀₊₁

= ²⁰C₁₀ (\( \dfrac{2}{3}x\))^20-10 (\( \dfrac{3}{2}x\))¹⁰

= ²⁰C₁₀

Hence, the middle term is ²⁰C₁₀.

Answered by Sakshi | 1 year ago