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`

If a_1,a_2, a_3, a_4 be the coefficient of four consecutive terms in the expansion of (1+x)^n , then prove that: (a_1)/(a_1+a_2)+(a_3)/(a_3+a_4)=(2a_2)/(a_2+a_3)dot

If a_1,a_2, a_3, a_4 be the coefficient of four consecutive terms in the expansion of (1+x)^n , then prove that: (a_1)/(a_1+a_2)+(a_3)/(a_3+a_4)=(2a_2)/(a_2+a_3)dot

If a_1,a_2, a_3, a_4 be the coefficient of four consecutive terms in the expansion of (1+x)^n , then prove that: (a_1)/(a_1+a_2)+(a_3)/(a_3+a_4)=(2a_2)/(a_2+a_3)dot

If a_1,a_2, a_3, a_4 be the coefficient of four consecutive terms in the expansion of (1+x)^n , then prove that: (a_1)/(a_1+a_2)+(a_3)/(a_3+a_4)=(2a_2)/(a_2+a_3)dot

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

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

If a_1, a_2 are the coefficients of x^n in the expansion of (1+x)^(2n) & (1+x)^(2n-1) respectively then a_1:a_2 will be

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)

If a_r is the coefficient of x^r in the expansion of (1+x)^n then a_1/a_0 + 2.a_2/a_1 + 3.a_3/a_2 + …..+n.(a_n)/(a_(n-1)) =