TAOCP 1.2.3 Exercise 2
By definition (2), $\sum_{1 \le j \le n} a_j$ denotes the sum of all terms $a_j$ for integer values of $j$ satisfying the condition $1 \le j \le n$.
Section 1.2.3: Sums and Products
Exercise 2. [01] What does the notation $\sum_{1 \le j \le n} a_j$ mean, if $n = 3.14$?
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By definition (2), $\sum_{1 \le j \le n} a_j$ denotes the sum of all terms $a_j$ for integer values of $j$ satisfying the condition $1 \le j \le n$.
If $n=3.14$, the integers satisfying $1 \le j \le 3.14$ are $j=1,2,3$. Therefore
$$ \sum_{1 \le j \le 3.14} a_j = a_1+a_2+a_3. $$
Hence the value is
$$ \boxed{a_1+a_2+a_3}. $$