Prove that identity : `sum_(i=1)^(n) (x_i-bar x)^2 = sum_(i=1)^(n) x_i^2-n bar x^2= sum_(i=1)^(n) x_i^2 -(sum_(i=1)^(n) x_i)^2/n` .

The sum and sum of squares corresponding to length x (in cm) and weight y (in gm) of 50 plant products are given below: sum_(i=1)^50 x_i=212, sum_(i=1)^50 x_i^2=902.8, sum_(i=1)^50 y_i=261, sum_(i=1)^50 y_i^2=1457.6 Which is more varying, the length or weight?

If sum_(i=1)^(n) cos theta_(i)=n , then the value of sum_(i=1)^(n) sin theta_(i) .

If sum_(i=1)^(n) cos theta_(i)=n , then the value of sum_(i=1)^(n) sin theta_(i) .

Let f(x)=x^2 + 3x-3,x leq 0 . If n points x_1, x_2, x_3,.....,x_n are so chosen on the x-axis such that (1) 1/n sumf^-1(x_i)=f(1/n sum_( i=1 )^nx_i) (2) sum_(i=1) ^ n f^-1(x_i)=sum_(i=1) ^ n x_i where f^-1 denotes the inverse of f, Then the AM of xi's is a)1 b)2 c)3 d)4

If (1+x+x^2+x^3)^n=sum_(r=0)^(3n)b_r x^r and sum_(r=0)^(3n)b_r=k ,"t h e n"sum_(r=0)^(3n)r b_r is

If Sigma_(i=1)^(2n) cos^(-1) x_(i) = 0 ,then find the value of Sigma_(i=1)^(2n) x_(i)

Evaluate : sum_(i=1)^18 (2^i +3^(i-1)) .

If the arithmetic mean of a_(1),a_(2),a_(3),"........"a_(n) is a and b_(1),b_(2),b_(3),"........"b_(n) have the arithmetic mean b and a_(i)+b_(i)=1 for i=1,2,3,"……."n, prove that sum_(i=1)^(n)(a_(i)-a)^(2)+sum_(i=1)^(n)a_(i)b_(i)=nab .

Prove that sum_(r=0)^n^n C_rsinr xcos(n-r)x=2^(n-1)sin(n x)dot

Prove that: adj.I_n^-1=I_n