MathDB

Let

2n

positive reals

a_1, a_2, \cdots, a_n, b_1, b_2, \cdots, b_n

satisfy

a_{i+1}\ge 2a_i

and

b_{i+1} \le b_i

for

1\le i\le n-1

. Find the least constant

C

that satisfy:

\displaystyle \sum^{n}_{i=1}{\frac{a_i}{b_i}} \ge \displaystyle \frac{C(a_1+a_2+\cdots+a_n)}{b_1+b_2+\cdots+b_n}

and determine all equality case with that constant

C

Problem Statement