Estimating Sum of Series as the Midpoint is a much better Approximation than the Partial Sum - Hive - YouTube - Notes - Playlist - Sequences and Series

In this video, I show that modifying our earlier Theorem 2 remainder estimate by adding the partial sum to both sides of the inequality provides a much better approximation than simply using the partial sum to approximate the sum of the series. This is because we now obtain an interval rather than just a simple sum. Taking the midpoint of the interval means that the maximum error is less than half the interval itself. I illustrate this by taking a second look at the series from Example 5, and show that with just 10 terms of the partial sum, we obtain the same accuracy that we had previously done with 32 terms.

#math #calculus #series #approximation #education

YouTube removed my 9/11 Jumper launched video, gave me a warning, require I take a policy training quiz, and is sending me self-help info.... 🤡▶️🤡▶️🤡▶️

Another epic 9/11 connection by @braingraft. This time showing that the 9/11 Jumpers are similar to the Tom Cruise movie "Vanilla Sky". 🌚🤯

20 years after 9/11, The Weather Channel publishes an article asking "what if Hurricane Erin hit the East Coast on 9/11?"

They also call the NASA satellite image of Erin with the 9/11 fumes visible as "one of the most chilling weather images ever taken".

Compare this sort of media attention vs early on when people were literally in disbelief when Dr. Judy Wood mentioned Hurricane Erin!

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