If `a_1,a_2,.....a_n` are positive real number whose product is a fixed number c, then the minimum value of `a_1+a_2+......+a_(n-1)+a_n` is

If a_(1),a_(2),a_(3),a_(4),...,a_(n) are n positive real numbers whose product is a fixed number c, then the minimum value of a_(1)+ a_(2) + ...+a_(n-1)+2a_(n) is-

If a_1. a_2 ....... a_n are positive and (n - 1) s = a_1 + a_2 +.....+a_n then prove that (a_1 + a_2 +....+a_n)^n ge (n^2 - n)^n (s - a_1) (s - a_2)........(s - a_n)

If a_1,a_2,a_3,.......a_n are in AP where a_1 gt 0foralli then the value of 1/(sqrta_1+sqrta_2)+1/(sqrta_2+sqrta_3)+....1/(sqrta_(n-1)+sqrta_n=

If a_1+a_2+a_3+......+a_n=1 AA a_i > 0, i=1,2,3,......,n , then find the maximum value of a_1 a_2 a_3 a_4 a_5......a_n .

If a_1 and a_2 are two non-collinear unit vectors and if |a_1+a_2|=sqrt(3) , then the value of (a_1-a_2)*(2a_1+a_2) is

If a_1,a_2,.....a_n are in H.P., then the expression a_1a_2 + a_2a_3 + ... + a_(n-1)a_n is equal to

Let vec r_1, vec r_2, vec r_3, .....vec r_n be the position vectors of points P_1,P_2, P_3 ,......P_n relative to the origin O . If the vector equation a_1 vec r_1+a_2 vec r_2+.....a_n vec r_n=0 hold, then a similar equation will also hold w.r.t. to any other origin provided a) a_1+a_2+......a_n=n b) a_1+a_2+....a_n=1 c) a_1+a_2+....a_n=0 d) a_1=a_2=a_3+a_n=0

If the sequence a_1, a_2, a_3,....... a_n ,dot forms an A.P., then prove that a_1^2-a_2^2+a_3^2-a_4^2+.......+ a_(2n-1)^2 - a_(2n)^2=n/(2n-1)(a_1^2-a_(2n)^2)

Find the number of all three elements subsets of the set {a_1, a_2, a_3, ........... a_n} which contain a_3dot

S.D. of numbers observation a_1, a_2, a_3,…..a_n is sigma then the S.D. of the observations lambdaa_1, lambdaa_2, lambdaa_3, lambdaa_3,....... lambdaa_n is