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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 `101 xx 1 = 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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