1.

(1+ x + x^(2))^(n) = a_(0) +a_(1)x + a_(2) x^(2) +...+ a_(2n )x^(2n) , thena_(0) a_(2n) - a_(1) a_(2r+1) + a_(2) a_(2r+2) - a_(3) a_(2r+3) +...+a_(2n-2r)a_(2n)= .

Answer»

0
1
`a_(n-r)`
`a_(n+r)`

Solution :On EQUATING the coefficients of `x^(2N +1)` on both sides
of (v) in illustration 25, we GET
`a_(0) a_(2n) - a_(1) a_(2r+1) + a_(2) a_(2r+2) - a_(3) a_(2r+3) +...+a_(2n-2r)a_(n+r)`.


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