the coefficient of x 3 in 3x2-2x2-x+1
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Answer:
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
Step-by-step explanation:
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