OHM’S THEOREM
OHM’S THEOREM 2.1 Martin Ohm Martin Ohm (May 6, 1792 - April 1, 1872) was a German mathematician who earned his doctorate in 1811 at Friedrich-Alexander-University, Erlangen-Nuremberg, under his advisor, Karl Christian von Langsdorf [1]. By the early 1800s he became a professor in the gymnasium at Thorn for mathematics and physics. In 1839, he was chosen to be a professor at the University of Berlin, and delivered lectures at the academy of architecture, and at the school of artillery and engineering [12]. 2.2 Ohm’s Rearrangement Theorem 2.2.1 Part I Theorem 2.2.1 ([11]). For p and q positive integers, rearrange ∑_(n≥1)^∞▒〖(-1)〗^(n-1)/n by taking the first positive terms, then the first q negative terms, then the next p positive terms, the next q negative terms, and so on. The rearranged series converges to ln〖(2)+1/2 ln(p/q) 〗. (2.1) Denote by A (p, q) the series resulting from this rearrangement. Let S_k be the partial sums of A (p, q) where specificall...