Daddy Summation!

Calculus Level 5

$\large{\sum _{ k=0 }^{ \infty }{ \frac { (4k)!(1103+26390k) }{ { (k!) }^{ 4 }{ 396 }^{ 4k } } } =\frac { A }{ \pi \sqrt { B } } }$

If the above summation can be expressed as shown above for some positive integers $A$ and $B$ , find $A+B$ .

The answer is 9809.

1 solution

Maximilian Wackenhuth
Feb 12, 2016

Ramanujan showed that the above sum times $\frac{ \sqrt{8} }{9801}$ is equal to $\frac{1}{\pi}$ . Therefor the solution is 9809.

It will become better off you show the proof

Department 8 - 5 years, 4 months ago

Lakshya don't you think this problem is a little difficult for the community?

Swapnil Das - 5 years, 4 months ago

Seriously?

Department 8 - 5 years, 4 months ago

@Department 8 – Yeah.. too difficult.

Swapnil Das - 5 years, 4 months ago

@Swapnil Das – So what should I do? I want this question appear to be easy.

Department 8 - 5 years, 4 months ago

@Department 8 – Write a wiki on concepts related to it.

Swapnil Das - 5 years, 4 months ago

If you really want to see a proof you can start here https://en.wikipedia.org/wiki/Ramanujan%E2%80%93Sato_series (I'm not quite sure if you are joking)

Maximilian Wackenhuth - 5 years, 4 months ago

Ramanujan makes me feel so dumb sometimes lol :)

i wonder how he found those formulas for $\pi$

Hamza A - 5 years, 4 months ago

Brilliant guy from birth.

Department 8 - 5 years, 4 months ago

Daddy Summation!

The answer is 9809.

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