If `a_i >0(i=1,2,3 n),` prove that `sum_(1lt=i

If a_i>0, i=1, 2, 3,..., n then prove that a_1/a_2+a_2/a_3+a_3/a_4+...+a_(n-1)/a_n+a_n/a_1gen .

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 .

If barx=1/n sum_(i=1)^n x_i then prove that sum_(i=1)^n (x_i-barx)=0

If a_i > 0 for i=1,2,…., n and a_1 a_2 … a_(n=1) , then minimum value of (1+a_1) (1+a_2) ….. (1+a_n) is :

If a_i>0,i=1,2,3,...n and (n-1)s=a_1+a_2+a_3+....+a_n , prove that a_1*a_2*a_3*....a_nge(n-1)^n*(s-a_1)(s-a_2)...(s-a_n) .

If sum_(i=1)^(2n)cos^(-1)x_(i)=0 , then sum_(i=1)^(2n)x_(i) is :

if sum_(i=1)^(n)a_(i)=0, where |a_(i)|=1,AA i then the value of sum_(1

If sum_(i=1)^(n)bar(a)_(i)=bar(0), where |bar(a)_(i)=1AA i, then the value of sum_(1<=i<=j<=n)bar(a)_(i)-bar(a)_(j) is

For any n positive numbers a_(1),a_(2),…,a_(n) such that sum_(i=1)^(n) a_(i)=alpha , the least value of sum_(i=1)^(n) a_(i)^(-1) , is

If I_(n)=int_(0)^( pi/4)tan^(n)xdx, prove that I_(n)+I_(n-2)=(1)/(n+1)