If a0,a1,a2,.... be the coefficients in...

If `a_0,a_1,a_2,....` be the coefficients in the expansion of `(1+x+x^2)^n` in ascending powers of x. prove that : `(i) a_0a_1-a_1a_2+a_2a_3-....=0`

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If a_(0),a_(1),a_(2),.... be the coefficients in the expansion of (1+x+x^(2))^(n) in ascending powers of x ,prove that : (i)a_(0)a_(1)-a_(1)a_(2)+a_(2)a_(3)-...=0

If a_(0), a_(1), a(2),… are the coefficients in the expansion of (1 + x + x^(2))^(n) in ascending powers of x, prove that a_(0) a_(2) - a_(1) a_(3) + a_(2) a_(4) - …+ a_(2n-2) a_(2n)= a_(n+1) .

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If a_0,a_1,a_2,……a_n be the successive coefficients in the expnsion of (1+x)^n show that (a_0-a_2+a_4……..)^2+(a_1-a_3+a_5………)^2=a_0+a_1+a_2+………..+a_n=2^n

The coefficient of x^(4) in the expansion of {sqrt(1+x^(2))-x}^(-1) in ascending powers of x when |x|<1, is 0 b.(1)/(2) c.-(1)/(2) d.-(1)/(8)

If a_1,a_2,a_3 and a_4 be any four consecutive coefficients in the expansion of (1+x)^n , prove that a_1/(a_1+a_2)+a_3/(a_3+a_4)= (2a_2)/(a_2+a_3)

The coefficients of x^n in the expansion of (1+x)6(2n) and (1+x0^(2n-1) are in the rtio of (A) 1:2 (B) 1:3 (C) 3:1 (D) 2:1

Prove that he coefficient of x^n in the expansion of (1+x)^(2n) is twice the coefficient of x^(n) in the expansion of (1+x)^(2n-1)

prove that the coefficient of x^(n) in the expansion of (1+x)^(2n) is twice the coefficient of x^(n) in the expansion of (1+x)^(2n-1)

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