END of the PI CHRONICLES

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.

 

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