Final answer:
The series 1 - 1/2 + 1/3 - 1/4 + ... can be written in sigma notation as Σ from n=1 to infinity of ((-1)^(n+1) / n), expressing the pattern of alternating positive and negative terms.
Step-by-step explanation:
The series 1 − 1/2 + 1/3 − 1/4 + … can be expressed in sigma notation as follows: Σn=1∞ ((-1)n+1 / n)
This is an alternating series, where the sign of the terms changes from positive to negative in a regular pattern. The n in the denominator represents the sequence of natural numbers, while ((-1)n+1) governs the alternating signs.