# Problems Plus 11: Solving Log Series Using a Telescoping Sum

in MES Science2 months ago

In this video I go over an infinite series that involves natural logarithms and can be solved by rearranging it into a form that allows for a Telescoping Sum to be applied. Recall that the Telescoping Sum is such that an infinite series has all terms cancel out except the first and the last term. When we rearrange, using log rules, the series, we see that it can be rewritten into terms whose individual terms are separate by an integer; which means they will cancel out with each successive series addition. Truly remarkable stuff!

The timestamps of key parts of the video are listed below:

• Problem 11: 0:00
• Solution: Simplifying using Logarithm Rules 0:18
• Telescoping Sum: 6:11
• Sum is - ln 2: 10:29

This video was taken from my earlier video listed below:

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▶️ 3Speak

Log problems back then in secondary school always difficult for me to assimilate

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