If for `n in I , n > 10 ;1+(1+x)+(1+x)^2++(1+x)^n=sum_(k=0)^n a_k*x^k , x!=0` then

If f(x)=sum_(k=0)^(n)a_(k)|x-1|^(k), where a_(i)in R, then

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 iun AP, find n.

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.

Evaluate: lim_ (n rarr oo) (1) / (n ^ (2)) sum_ (k = 0) ^ (n-1) [k int_ (k) ^ (k + 1) sqrt ((xk) (k + 1-x)) dx]

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

lim_ (n rarr oo) n sum_ (k = 0) ^ (n-1) sum_ (k = 0) ^ (n-1) int _ ((k) / (n)) ^ ((k + 1) / ( n)) sqrt ((x- (k) / (n)) ((k + 1) / (n) -x)) dx is (pi) / (k) then k