Let `f(n)=sum_(k=1)^(n) k^2(n C_k)^ 2` then the value of f(5) equals

Given (1-x^(3))^(n)=sum_(k=0)^(n)a_(k)x^(k)(1-x)^(3n-2k) then the value of 3*a_(k-1)+a_(k) is

Let s_(n) denote the sum of first n terms of an A.P. and S_(2n) = 3S_(n) . If S_(3n) = kS_(n) then the value of k is equal to

Let f be a continuous function on R such that f (1/(4n))=sin e^n/(e^(n^2))+n^2/(n^2+1) Then the value of f(0) is

Let S_n=sum_(k=1)^(4n)(-1)(k(k+1))/2k^2dot Then S_n can take value (s) 1056 b. 1088 c. 1120 d. 1332

Find sum_(k=1)^(n)(1)/(k(k+1)) .

Statement1: if n in Na n dn is not a multiple of 3 and (1+x+x^2)^n=sum_(r=0)^(2n)a_r x^r , then the value of sum_(r=0)^n(-1)^r a r^n C_r is zero Statement 2: The coefficient of x^n in the expansion of (1-x^3)^n is zero, if n=3k+1orn=3k+2.

If alpha=e^(i2pi//7)a n df(x)=a_0+sum_(k-0)^(20)a_k x^k , then prove that the value of f(x)+f(alpha, x)+......+f(alpha^6x) is independent of alphadot

The function f(x)=sum_(k=1)^5 (x-K)^2 assumes then minimum value of x given by (a) 5 (b) 5/2 (c) 3 (d) 2