Finding An Infinite Sum | Calculus

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[williamperez-hernandez]

Known as Leibniz Series for Pi. However, it was discovered by Madhava (or his "students") from India in 14-15th century. In 1671 it was by James Gregory, then by Leibniz in 1673. Starting from the Taylor Series for arctan x, it is easily obtained. This, however, needs Calculus. How did Madhava obtain this result 200-300 years before the invention of Calculus? Being very SMART.

[mbmillermo]

Fun facts: The 1/(1+x)² function is the kernel of a Cauchy density which is also the density of a t-distribution on one degree of freedom. I like your videos!

[omoyne]

There are no boundaries to Mathematics.... and so to its beauty ❤🎉

[stvp]

I love how the pops in as soon as he says “uh-oh” 😄

[eckhardfriauf]

I noticed that you write 7 with an extra horizontal line through the digit. Possibly to distinguish it from the digit 1. As I am German, I sure appreciate it. But it is quite uncommon in the US or so. Any explanation why you prefer the extra horizontal line version?

[mihaleben]

Fun fact: adding up decimals makes them smaller

[VSN]

kinda cheated on this since I knew the Taylor of arctan(x) beforehand

[leif]

So it is not possible to solve this without calculus?

[manoharkanade]

Please tell us how int of (1/ 1+x2) is arch tan

[fabriziosantin]

The geometric series converges for r between 0 and 1... but the upper bound of the integral is 1... so what happens there?

[Ssilki_V_Profile]

1-1/3+1/5-1/7... Is non stable sum. Rearanging plus or minus terms may give you diferent results.

[hamid-sir_NSC_CLASSES]

Nice. physics for xi. Xii. NEET IIT jee join n s c physics class by Dr Hamid sir bilkul free in English medium. Hindi medium. Hinglish medium

[zawatsky]

Каждый раз меньше прибавляется, но и меньше отнимается. В итоге эта синусоида сходит в ноль, следовательно, выражение стремится к единице, ну или около того.