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If (1 + x + x^2)^n = a0 + a1x + a2x^2 + ...... + a2nx^2n, then a0 – a1 + a2 – a3 + ..... + a2n is equal to

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If (1 + x + x2)n = a0 + a1x + a2x2 + ...... + a2nx2n, then a0 – a1 + a2 – a3 + ..... + a2n is equal to

(a) 0 

(b) 1 

(c) 2n

(d) 2nCn

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1 Answer

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Answer : (b) 1

Given, (1 + x + x2)n = a0 + a1x + a2x2 + ..... + a2n x2 

Putting x = –1 in the above equation, we have 

(1 – 1 + 1)n = a0 – a1 + a2 – a3 + ..... + a2n 

⇒ a0 – a1 + a2 – a3 + ..... + a2n = 1n 

= 1.

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