Series to Ad Infinitum part III

Calculus Level 4

112123+134= ?\displaystyle{ \dfrac{1}{1\cdot 2} -\dfrac{1}{2\cdot 3} +\dfrac{1}{3\cdot 4} - \cdots = \text{ ?} }

Answer up to 44 decimal places.

Image Credit: Wikipedia Natural Logarithm by W. Muła
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