" 8.Show that "sum_(I)=1n^(2)(m)/(18)=5

Show that sum_(r=1)^(9)sin^(2)((r pi)/(18))=5

Show that sum_(n=1)^(25) (i^(n) + i^(n +1)) = i-1

Ifx_(1),x_(2),....x_(n) are n observations such that sum_(i=1)^(n)(x_(i))^(2)=400 and sum_(i=1)^(n)x_(i)=100 then possible values of n among the following is (1)18(2)20(3)24(4)27

Let x_(1),x_(2),...,x, are n observations such that sum_(i=1)^(t)x_(1)=10 and sum_(i=1)^(n)x_(i)^(2)=260 and standard deviation is 5 then n is equal to

Show that sum_(k=m)^n ^kC_r=^(n+1)C_(r+1)-^mC_(r+1)

Show that sum_(k=m)^n ^kC_r=^(n+1)C_(r+1)-^mC_(r+1)

sum_(j=1)^(n)sum_(i=1)^(n)i=

If sum_(i=1)^(18)(x_(i)-8)=9 and sum_(i=1)^(18)(x_(i)-8)^(2)=45 then find the standard deviation of x_1 , x_2, ....,x_(18)

IfI_(m , n)=int_0^(pi/2)sin^m xcos^n xdx , Then show that I_(m , n)=(m-1)/(m+n)I_(m-2,n)(m ,n in N) Hence, prove that I_(m , n)=f(x)={((n-1)(n-3)(m-5)(n-1)(n-3)(n-5))/((m+n)(m+n-2)(m+n-4))pi/4 when both m and n are even ((m-1)(m-3)(m-5)(n-1)(n-3)(n-5))/((m+n)(m+n-2)(m+n-4))}

IfI_(m , n)=int_0^(pi/2)sin^m xcos^n xdx , Then show that I_(m , n)=(m-1)/(m+n)I_(m-2,n)(m ,n in N) Hence, prove that I_(m , n)=f(x)={((n-1)(n-3)(m-5)(n-1)(n-3)(n-5))/((m+n)(m+n-2)(m+n-4))pi/4 when both m and n are even ((m-1)(m-3)(m-5)(n-1)(n-3)(n-5))/((m+n)(m+n-2)(m+n-4))}