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Question

If a0,a1,a2,.... be the coefficients in the expansion of (1+x+x2)n in ascending powers of x, then a0a1−a1a2+a2a3−....=

A
0
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B
1
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C
2
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D
1
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Solution

The correct option is C 0
(1+x+x2)n=a0+a1x+a2x2.....+anxn
Let n=1 in the above expression, thus as we can see from the expression,
the values of a0=1
also, a1=1
a2=1 and so on...
Thus, the value of
a0a1a1a2+a2a3..........=11+11+1.....
Therefore, a0a1a1a2+a2a3..........=0
Thus the correct answer is 0

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