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If (1+x-2x^2)^6=1+a1 x+a2 x^2+a2 x^3+......

If `(1+x-2x^2)^6=1+a_1 x+a_2 x^2+a_2 x^3+.........`, then the value of `a_2+a_4+a_6+......+a_12` will be

Text Solution

Verified by Experts

The correct Answer is:
31
`(1+x-2x^(2))^(6) = 1+a_(1)x+a_(2)x^(2)+"…."+a_(12)x^(12)`
Putting `x = 1` and `x = - 1` and adding the results, we get
`64 = 2(1+a_(2)+a_(4)+"….")`
`:. a_(2)+a_(4)+a_(6)+"…."a_(12) = 31`
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