Question 183
On a given street, there are $n$ houses numbered from $1$ to $n$. Let $a_{i}$ ($1 \leq i \leq n$) be the number of people living in the house numbered $i$, and let $b_{i}$ ($i \geq 1$) be the number of houses on the street in which at least $i$ people live. Prove that
$$
a_{1}+a_{2}+\cdots+a_{n}=b_{1}+b_{2}+b_{3}+\cdots
$$
$$
a_{1}+a_{2}+\cdots+a_{n}=b_{1}+b_{2}+b_{3}+\cdots
$$