Write the sum using sigma notation: \[ \begin{array}{l} 1+2+3+4+\cdots+137=\sum_{n=1}^{A} B, \text { where } \\ A= \\ B= \end{array} \]

Step 1 ：The problem is asking to express the sum of the series 1+2+3+4+...+137 in sigma notation.

Step 2 ：In sigma notation, the sum of the first n natural numbers is represented as \(\sum_{i=1}^{n} i\).

Step 3 ：Here, the series goes up to 137, so n (or A in the question) is 137.

Step 4 ：The term being summed (B in the question) is simply the index i.

Step 5 ：So, we can write the sum as \(\sum_{i=1}^{137} i\).

Step 6 ：\(\boxed{A = 137, B = i}\). So, the sum can be written as \(\sum_{i=1}^{137} i\).