MathDB

Let

b_1

\dots

b_n

be nonnegative integers with sum

2

and

a_0

a_1

\dots

a_n

be real numbers such that

a_0=a_n=0

and

|a_i-a_{i-1}|\leq b_i

for each

i=1

\dots

n

. Prove that

\sum_{i=1}^n(a_i+a_{i-1})b_i\leq 2

I believe that the original problem was for nonnegative real numbers and it was a typo on the version of the exam paper we had but I'm not sure the inequality would hold

Problem Statement