`(a_1)/(a_1+a_2)+(a_3)/(a_3+a_4)=(2a_2)/(a_2+a_3)`

If the coefficient of-four successive termsin the expansion of (1+x)^n be a_1 , a_2 , a_3 and a_4 respectivel. Show that a_1/(a_1+a_2)+a_3/(a_3+a_4)=2 a_2/(a_2+a_3)

If a_1,a_2,a_3,a_4 are the coefficients of 2nd, 3rd, 4th and 5th terms of (1+x)^n respectively then (a_1)/(a_1+a_2) , (a_2)/(a_2+a_3),(a_3)/(a_3+a_4) are in

If (a_2a_3)/(a_1a_4) = (a_2+a_3)/(a_1+a_4)=3 ((a_2 -a_3)/(a_1-a_4)) then a_1,a_2, a_3 , a_4 are in :

If (a_2a_3)/(a_1a_4) = (a_2+a_3)/(a_1+a_4)=3 ((a_2 -a_3)/(a_1-a_4)) then a_1,a_2, a_3 , a_4 are in :

Prove that ((a_1)/(a_2)+(a_3)/(a_4)+(a_5)/(a_6)) ((a_2)/(a_1)+(a_4)/(a_3)+(a_6)/(a_5)) geq 9

If (a_2 a_3)/(a_1 a_4) = (a_2 + a_3)/(a_1 + a_4) = 3 ((a_2 - a_3)/(a_1 - a_4)) then a_1, a_2, a_3, a_4 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

prove that |(1/(a-a_1)^2,1/(a-a_1),1/a_1),(1/(a-a_2)^2,1/(a-a_2),1/a_2),(1/(a-a_3)^2,1/(a-a_3),1/a_3)|=(-a^2(a_1-a_2)(a_2-a_3)(a_3-a_1))/(a_1a_2a_3(a-a_1)^2(a-a_2)^2(a-a_3)^2) .

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_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