Question

Find the sum of the coefficients in the expansion of (1+2x-3x^2)^5

Answer 1

Answer:

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Step-by-step explanation:

Consider the given series.

(1+2x+3x

2

+.....)

2

−3

Let,

S=1+2x+3x

2

+4x

3

...... ……(1)

xS=x+2x

2

+3x

3

+4x

4

+... ……(2)

Subtract equation (2) from equation (1), we get

S−xS=(1)+(2−1)x+(3−2)x

2

+(4−3)x

3

+...

S(1−x)=1+x+x

2

+x

3

+…....=

1−x

1

s=

(1−x)

2

1

=(1−x)

−2

s

−

2

3

=[(1−x)

−2

]

2

−3

=(1−x)

3

s

2

−3

=(1−x)

3

=1−x

2

−3x+3x

2

Therefore, coefficient of x

5

is zero