If `a_1,a_2,….a_n` are in H.P then `(a_1)/(a_2+,a_3,…,a_n),(a_2)/(a_1+a_3+….+a_n),…,(a_n)/(a_1+a_2+….+a_(n-1))`
are in

If a_1, a_2, ,a_n >0, then prove that (a_1)/(a_2)+(a_2)/(a_3)+(a_3)/(a_4)++(a_(n-1))/(a_n)+(a_n)/(a_1)> n

If a_1,a_2,a_3….a_(2n+1) are in A.P then (a_(2n+1)-a_1)/(a_(2n+1)+a_1)+(a_2n-a_2)/(a_(2n)+a_2)+....+(a_(n+2)-a_n)/(a_(n+2)+a_n) is equal to

If a_1,a_2,a_3…a_n are in H.P and f(k)=(Sigma_(r=1)^(n) a_r)-a_k then a_1/f(1),a_2/f(3),….,a_n/f(n) are in

If (1 + ax + b x^2)^4 = a_0 +a_1 x + a_2 x^2 +...+a_8 x^8 when a,b,a_0,a_1,a_2...,a_8 in R such that a_0+a_1+a_2 != 0 and |(a_0,a_1,a_2),(a_1,a_2,a_0),(a_2,a_0,a_1)|=0 then the value of 5a/b (A) 6 (B) 8 (C) 10 (D) 12

Let a_1,a_2,a_3…., a_49 be in A.P . Such that Sigma_(k=0)^(12) a_(4k+1)=416 and a_9+a_(43)=66 .If a_1^2+a_2^2 +…+ a_(17) = 140 m then m is equal to

If a ,a_1, a_2, a_3, a_(2n),b are in A.P. and a ,g_1,g_2,g_3, ,g_(2n),b . are in G.P. and h s the H.M. of aa n db , then prove that (a_1+a_(2n))/(g_1g_(2n))+(a_2+a_(2n-1))/(g_1g_(2n-1))++(a_n+a_(n+1))/(g_ng_(n+1))=(2n)/h

If a_1,a_2,a_3 ,….""a_n is an aritmetic progression with common difference d. prove that tan [ tan ^(-1) ((d)/( 1+ a_1a_2))+ tan^(-1) ((d)/(1+a_2a_3))+…+((d)/(1+a_n a_( n-1))) ] = (a_n -a_1)/(1 +a_1 a_n )

If S+a_1+a_2+a_3++a_n ,a_1 in R^+ for i=1ton , then prove that S/(S-a_1)+S/(S-a_2)++S/(S-a_n)geq(n^2)/(n-1),AAngeq2

Let a_1,a_2,.........a_n be real numbers such that sqrt(a_1)+sqrt(a_2-1)+sqrt(a_3-2)++sqrt(a_n-(n-1))=1/2(a_1+a_2+.......+a_n)-(n(n-3)/4 then find the value of sum_(i=1)^100 a_i

Let a_1,a_2…….a_n be fixed real number such that f(x)=(x-a_1)(x-a_2)……….(x-a_n) what lim_(x to a) f(x) For a ne a_1,a_2……a_n compute lim_(x to 0) f(x)