Alternating Near Harmonic Series?

Calculus Level 1

\[ \large 4 \times \left [ 1 - \frac 1 3 + \frac 1 5 - \frac 1 7 + \ldots \right ] = \ ? \]

Details and Assumptions:

  • \( \pi\) is the ratio of circumference to diameter of a circle.

  • \(G\) denote the Gravitational constant.

  • \( \gamma\) denote Euler-Mascheroni constant.

  • \(\hbar\) denote Planck constant.

Image Credit: Wikimiedia Apple Pie by Scott Bauer
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