The coefficient of t4 in the expansion of is

Engineering

Mathematics

Binomial Theorem for Negative and Fractional Index

Question

The coefficient of t⁴ in the expansion of ${(\frac{1 - t^{6}}{1 - t})}^{3}$ is

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(1–t⁶)³ (1-t)^–3

(1–t¹⁸ – 3t⁶ + 3t¹²) (1–t)^–3

⇒ coefficient of t⁴ in (1–t)^–3 is ^3+4-1C₄ = ⁶C₂ = 15