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  • Stuck here, help me understand: - The coefficient of in the expansion of is: - Binomial theorem and its simple applications - JEE Main

 

The coefficient of t^{4} in the expansion of \left ( 1-t^{6}/1-t \right )^{3} is:

  • Option 1)

     

    12

  • Option 2)

     

    14

  • Option 3)

     

    15

  • Option 4)

     

    10

Answers (1)

best_answer

 

General Term in the expansion of (x+a)^n -

T_{r+1}= ^{n}c_{r}\cdot x^{n-r}\cdot a^{r}
 

- wherein

Where r\geqslant 0 \, and \, r\leqslant n

r= 0,1,2,----n

 

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

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

Coefficient of t^4 in (1-t)^{-3} is ^{3+4 -1}C_4 = ^6C_2 = 15


Option 1)

 

12

Option 2)

 

14

Option 3)

 

15

Option 4)

 

10

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