Relation between Coefficient and Indices of x and y
if a0 , a...
Question
if a0,a1,a2....be the coefficients in the expansion of (1 + x + x2)n in ascending powers f x , then prove that : a0+a1+a2+....+an−1=13(3n−an)
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Solution
Putting x = 1 in (1), we get a0+a1+a2+....+ar+.....+a2n=3n ......(2) Since ar=a2n−r i.e. a0=a2n,a1=a2n−1 etc. 2(a0+a1+a2+....+an−1)+an=3n ∴a0+a1+a2+....+an−1=12(3n−an)