I did figure a sixth term in the arcsin series, and so it yields:

1 + 0.17 + 0.08 + 0.04 + 0.02 + 0.016 + …

This is supposed to yield one-half of π . I bet Leibnitz saw how unwieldy this series is!!! We are up to the eleventh derivative, and the factorial is 40 million or so. OK, THE ARCTAN DOES YIELD A SIMPLY EXPRESSIBLE SERIES, WHICH THIS IS NOT.

Look at: π/4 as 1 – 1/3 + 1/5 – 1/7 + … and I like to combine pairs of terms by common denominator: 1 -2/15 – 2/63 – … This is quicker, more concise.

I am satisfied, having never seen these things before. Better late than never, and lo, I bloom late at age 67.

Advertisements