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If (1+ x + x ^(2) ""x ^(100))(1- x+x ^(2...

If `(1+ x + x ^(2) "_____"x ^(100))(1- x+x ^(2) - x ^(3) +"____"+x ^(150))`
`=a _(0) + a_(1) x + a_(2)x^2 + "___"+a _(250)x ^(250)`
Then the value of `a _(0) + a _(2) + a_(4) +"____"+ a_(250)` is equal to `"____".`

Text Solution

Verified by Experts

The correct Answer is:
126
Put `x =1` we get `1-1 xx1 = a_(0) + a_(1) + a_(2)"___"+ a_(250)`
Put `x =-1 ` we get `1xx151 =a_(0) -a_(1) +a_(2) "___"a _(250)`
`252 =2 (a _(0) + a _(2)+"____"a _(250))`
`a _(0) + a_(2) + a_(4)+"___"+a _(250)=126`
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