1.

Find the coefficient of x4 in the expansion of (1 + x + x2 + x3)11​

Answer»

Answer:

x

4

can be achieved in the following ways:

x

4

.1

n−4

.(x

2

)

0

.(x

3

)

0

Hence, COEFFICIENT will be

n

C

4

​

.

x

2

.1

n−3

.(x

2

)

1

.(x

3

)

0

Hence, coefficient will be 3

n

C

3

​

.

x

1

.1

n−2

.(x

2

)

0

.(x

3

)

1

Hence, coefficient will be 2

n

C

2

​

.

x

0

.1

n−2

.(x

2

)

2

.(x

3

)

0

Hence, coefficient will be

n

C

2

​

.

Hence, the required coefficient will be

n

C

4

​

+3

n

C

3

​

+3

n

C

2

​

=

n

C

4

​

+3(

n

C

3

​

+

n

C

2

​

).

=

n

C

4

​

+3(

n+1

C

3

​

).

=

n

C

4

​

+

n

C

2

​

+

n

C

1

​

.

n

C

2

​

Step-by-step explanation:


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