Calculate and plot Ramanujan-Sato Series?

Questions
,
1

Hello,
For a math assignment I am evaluating different values for pi and plotting them into a table.
One formula that I have to use is the Ramanujan-Sato series.
For some reason, when I set it to calculate it puts the same value in the table ‘i’ amount of times.

Tab3 = Table[1/N[(2*(Sqrt[2]/99^2))*
           Sum[((4*i)!/i!^4)*((26390*i + 1103)/396^(4*i)), 
             {i, 0, k}]], {k, 100}]

sato.png

I have to add the value for each summation step into a table and then plot that table. I don’t understand why this isn’t working and neither does my supervisor, any help would be greatly appreciated.

2

The value 100 for k is rather high!
And you should take into account, that every iteration adds about 8 correct digits:

Column[Table[
  1/N[(2*(Sqrt[2]/99^2))*
     Sum[((4*i)!/i!^4)*((26390*i + 1103)/396^(4*i)), {i, 0, k}], 
    9 + k 8], {k, 8}]]

output.png
output.png518×133 1.57 KB

3

Thank you for the help :smiley: