∑(n=1 to ∞) ((-1)^n/n))
Definition
This particular notation represents an infinite alternating harmonic series. In this case, each term alternates between positive and negative with diminishing magnitudes inversely proportional to n.
Analogy
Imagine you have a never-ending roller coaster where every other seat is empty. As the ride progresses, each occupied seat moves up and down, with the height of their movement gradually decreasing.
Related terms
Harmonic series: A series that has terms in the form of 1/n, where n represents positive integers.
Geometric series: A series that has terms in the form of a constant multiplied by an exponent raised to powers of n.
Convergence tests: Various methods used to determine whether or not an infinite series converges or diverges. Examples include the comparison test and ratio test.
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