prove $\bigcup_{n=1}^\infty A_n=\bigcup_{n=1}^\infty B_n$ prove$\bigcup_{n=1}^\infty A_n=\bigcup_{n=1}^\infty B_n$ if $A_i$ is a arbitrary set and $B_1=A_1$ and $B_n=A_n-\bigcup_{i=1}^{n-1} A_i$ for $n\ge 2$.
I have no ideas for solving it there was another question befor this that wanted to show:
$A_n\cap[A_n\cup B_n]=A_n$ that was easy to solve because $A_n\cup B_n=B_n$ and then $B_n \cap A_n=A_n$.I wrote this because I think it may helpful.
Thanks for your answers. 

A start: The right-hand side is clearly a subset of the left-hand side, because $B_n\subseteq A_n$.
To show that the left-hand side is a subset of the right-hand side, pick an element $x$ of the left-hand side. Then there is a smallest $n$ such that $x\in A_n$. Use this to show $x$ is in the RHS.
