If the coefficients of 4 consecutive terms in the expansion of `(1+x)^(n)` are `a_(1),a_(2),a_(3),a_(4)` respectively, then show that
`(a_(1))/(a_(1)+a_(2))+(a_(3))/(a_(3)+a_(4))=(2a_(2))/(a_(2)+a_(3))`

If the coefficients of the consicutive four terms in the expansion of (1+x)^(n)" be "a_(1),a_(2),a_(3)and a_(4) respectively , 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) be the coefficient of four consecutive terms in the expansion of (1+x)^(n), then prove that: (a_(1))/(a_(1)+a_(2))+(a_(3))/(a_(3)+a_(4))=(2a_(2))/(a_(2)+a_(3))

If a_(1),a_(2),a_(3)anda_(4) be the coefficients of four consecutive terms in the expansion of (1+x)^(n) , then prove that (a_(1))/(a_(1)+a_(2)),(a_(2))/(a_(2)+a_(3))and(a_(3))/(a_(3)+a_(4)) are in A.P.

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_(n) are in HP, than prove that a_(1)a_(2)+a_(2)a_(3)+a_(3)a_(4)+"....."+a_(n-1)a_(n)=(n-1)a_(1)a_(n)

If a_(1),a_(2),a_(3),".....",a_(n) are in HP, than prove that a_(1)a_(2)+a_(2)a_(3)+a_(3)a_(4)+"....."+a_(n-1)a_(n)=(n-1)a_(1)a_(n)

If a_(1),a_(2),a_(3),".....",a_(n) are in HP, than prove that a_(1)a_(2)+a_(2)a_(3)+a_(3)a_(4)+"....."+a_(n-1)a_(n)=(n-1)a_(1)a_(n)

If a_(1),a_(2),a_(3),".....",a_(n) are in HP, than prove that a_(1)a_(2)+a_(2)a_(3)+a_(3)a_(4)+"....."+a_(n-1)a_(n)=(n-1)a_(1)a_(n)