## 2018 NT exam P2

Discussion on Bangladesh National Math Camp
Ananya Promi
Posts: 36
Joined: Sun Jan 10, 2016 4:07 pm
Let $a_1, a_2, ....., a_n$ be a sequence of real numbers such that $a_1+a_2+......a_n=0$ and define $b_i=a_1+a_2+......a_i$ for $$1\leq i \leq n$$. Suppose that $$b_i(a_{j+1}-a_{i+1})\geq 0$$ for all $$1\leq i \leq j \leq n-1$$. Show that
max |$a_l$| $\geq$ max |$b_m$|
$(1 \leq l \leq n)$ and $(1 \leq m \leq n)$