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If (1 + x + 2x^2)^20 = a0 + a1x + a2 x^2 + a3x^3 +.......+ a40x^40, then a0 + a2 + a4 +........+ a38 is equal to

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If (1 + x + 2x2) 20 = a0 + a1x + a2 x2 + a3x3  +.......+ a40x40, then a0 + a2 + a4 +........+ a38 is equal to 

(a)   219(220 – 1) 

(b)   220(219 – 1)

(c)   219(220 + 1)

(d)   none of these 

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1 Answer

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Best answer

Correct option (a)  219(220 – 1)

Explanation: 

Put x = 1 and x = –1 and adding we get 420+220 = 2(a0 + a2 + a4 +....+ a38 + a40)

⇒ 239 + 219 = a0 + a2  + ..... + a38 + 220 

∴ a0 + a2 + a4 +.....+ a38 

=239 + 219 – 220 

= 219(220 + 1– 2)

= 219(220 – 1)

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