The coefficient of t 4 in the expansion of 1 - t 6 1 - t 3 is

1 - t 6 1 - t 3 = 1 - t 6 3 1 - t - 3 = 1 - t 18 - 3 t 6 + 3 t 12 1 - t - 3 ∴ Co-efficient of t 4 = 1 × 3 + 4 - 1 C 4 = 6 C 4 = 15

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Mathematics - Binomial Theorem Question with Solution | TestHub

MathematicsBinomial TheoremBinomial Theorem for Negative IndexMedium2 minPYQ_2019

MathematicsMediumsingle choice

The coefficient of $t^{4}$ in the expansion of ${(\frac{1 - t^{6}}{1 - t})}^{3}$ is

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Answer:

Solution:

${(\frac{1 - t^{6}}{1 - t})}^{3} = {(1 - t^{6})}^{3} {(1 - t)}^{- 3}$

$= (1 - t^{18} - 3 t^{6} + 3 t^{12}) {(1 - t)}^{- 3}$

$∴$ Co-efficient of $t^{4} = 1 \times^{3 + 4 - 1} C_{4} =^{6} C_{4} = 15$

Stream:JEESubject:MathematicsTopic:Binomial TheoremSubtopic:Binomial Theorem for Negative Index

⏱ 2mℹ️ Source: PYQ_2019

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