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In this video I go over a pretty amazing infinite series and show, after an extensive math proof, that it equals to ln 2. The series is sum of the infinite terms that follow the pattern 1/(12) + 1/(34) + 1/(5*6) + ... etc., and somehow this equals to the simple answer of ln 2 or natural log of 2. While the proof is complicated, fortunately the problem has 4 parts to provide the steps to solving for the proof. The steps involve writing a geometric series as an integral and then determining an inequality from solving the definite integral from x = 0 to x = 2 which includes ln 2 in the result. Rearranging the inequality and we obtain our final answer of ln 2. Amazing stuff!
The timestamps of key parts of the video are listed below:
This video was taken from my earlier video listed below:
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