The number of terms in the expansion of (x^2-2+1/x^2)^6 is?
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The number of terms in the expansion of (x^2-2+1/x^2)^6 is?
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Answer:
S=(1+5
2
x)
9
+(1−5
2
x)
9
Let k=5
2
Then the above binomial expansion changes to
S=(1+k)
9
+(1−k)
9
=[1+
9
C
1
k+
9
C
2
k
2
+...
9
C
9
k
9
]+[1−
9
C
1
k+
9
C
2
k
2
−
9
C
3
k
3
...−
9
C
9
k
9
]
=2[1+
9
C
2
k
2
+
9
C
4
k
4
+
9
C
6
k
6
+
9
C
8
k
8
]
Hence in total 5 terms will be there.