Notation: where to put brackets around summation or product, what is the convention? Sometimes it is necessary to place brackets around a long summation or product. If I am forced to do so, do I place them around the whole summation or product, $$\left(\sum_{n=1}^N a_n + b\right), \;\text{and }\; \left(\prod_{n=1}^N\frac{1}{2}d_n\right),$$
or inside the summation or product
 $$\sum_{n=1}^N \left(a_n + b\right), \;\text{and } \;\prod_{n=1}^N\left(\frac{1}{2}d_n\right).$$
I've seen both in articles, but is one method preferred over the other?
Edit: I removed possible disambiguation 
 A: 
The scope of the sigma operator $\Sigma$ and the product operator $\Pi$ are solely defined via arithmetic precedence rules. 
  
  
*
  
*Sum: The scope is given by the expression that follows immediately the $\sum$ and is valid respecting the arithmetic precedence rules up to an operator with precedence level equal to '$+$' or up to the end if no such operator follows.
  
*Product: The scope is given by the expression that follows immediately the $\prod$ and is valid respecting the arithmetic precedence rules up to an operator with precedence level equal to '$\cdot$' or up to the end if no such operator follows.
  

This implies that

\begin{align*}
\left(\sum_{n=1}^N a_n + b\right)&=a_1+a_2+\cdots+a_N+b\\
&=\sum_{n=1}^N a_n + b\\
\sum_{n=1}^N \left(a_n + b\right)&=\left(a_1+b\right)+\left(a_2+b\right)\cdots+\left(a_N+b\right)\\
&=\sum_{n=1}^N a_n + Nb\\
\end{align*}

as well as

\begin{align*}
\left(\prod_{n=1}^N\frac{1}{2}d_n\right)&=\underbrace{\frac{1}{2}\cdot\frac{1}{2}\cdots\frac{1}{2}}_{N\text{ times}}\cdot d_n\\
&=\frac{d_n}{2^N}\tag{1}\\
\prod_{n=1}^N\left(\frac{1}{2}d_n\right)&=\left(\frac{1}{2}d_1\right)\cdot\left(\frac{1}{2}d_2\right)\cdots\left(\frac{1}{2}d_N\right)\\
&=\frac{1}{2^N}\prod_{n=1}^Nd_n\tag{2}\\
\end{align*}
Of course it is a bad style in (1) to use a free variable $d_n$ with the same index as for the product index. This notation would rather indicate a typo where the author had a bracketing as in (2) in mind.

Hint: You might find chapter 2: Sums in Concrete Mathematics by R.L. Graham, D.E. Knuth and O. Patashnik helpful. It provides a thorough introduction into the usage of sums.
