If `|a_k|< 3, 1 le k le n,` then all complex numbers `z` satisfying equation `1+a_1z+a_2z^2+..........+a_nz^n=0`

If a_k=1/(k(k+1)) for k=1 ,2……..,n then prove that (sum_(k=1)^n a_k)^2 =n^2/(n+1)^2

If a_k is the coefficient of x^k in the expansion of (1+x+x^2)^n for k = 0, 1, 2, ......., 2n then a_1+2a_2+3a_3+...+2na_(2n)=

If a_k is the coefficient of x^k in the expansion of (1 +x+x^2)^n for k = 0,1,2,……….,2n then a_1 +2a_2 + 3a_3 + ………+2n.a_(2n) =

If a_k is the coefficient of x^k in the expansion of (1 +x+x^2)^n for k = 0,1,2,……….,2n then a_1 +2a_2 + 3a_3 + ………+2n.a_(2n) =

Let (1+x^2^2)^2(1+x)^n = sum _(k=0)^(n+4)a_k x^k. If a_1,a_2,a_3 are in rithmetic progression find n.

Let (1+x^2)^2(1+x)^n=sum_(k=0)^(n+4)a_k x^k . If a_1 , a_2 and a_3 are in arithmetic progression, then the possible value/values of n is/are a. 5 b. 4 c. 3 d. 2

Let (1+x^2)^2(1+x)^n=sum_(k=0)^(n+4)a_k x^k . If a_1 , a_2 and a_3 are in arithmetic progression, then the possible value/values of n is/are a. 5 b. 4 c. 3 d. 2

Let (1+x^2)^2(1+x)^n=sum_(k=0)^(n+4)a_k x^k . If a_1 , a_2 and a_3 are in arithmetic progression, then the possible value/values of n is/are