Sums of Reciprocals of TwoTerm Squares
Table
(02/09/2010)





















































The above table shows for each value of m and n the results of (I) converge to a form of, where r, p and q are integers. As m and n are very large values, (I) converges to small numbers or tends to zero. This means that we obtain many square roots of ratios of rational numbers that give approximate to Pi, namely
.
For example, we consider the given series with m = 8 and n = 9 from the above table, give
.
The Pi approximation can be computed by using (II) as follows
, which is good for 3 digits.
Other Similar Series
Tables
Sums of Reciprocals of TwoTerm Cubes Table, Sums of Reciprocals of TwoTerm Fourth Powers Table, Sums of Reciprocals of TwoTerm Fifth Powers Table
InText or Website Citation
Tue N. Vu, Sums of Reciprocals of TwoTerm Squares Table, 02/09/2010, from Series Math Study Resource.
Hyperlink: www.seriesmathstudy.com/sumreciprocalsoftwotermsquares.htm.
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