Sums of Reciprocals of Two-Term 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

 

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For example, we consider the given series with m = 8 and n = 9 from the above table, give

 

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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 Two-Term Cubes Table, Sums of Reciprocals of Two-Term Fourth Powers Table, Sums of Reciprocals of Two-Term Fifth Powers Table

 

In-Text or Website Citation

Tue N. Vu, Sums of Reciprocals of Two-Term Squares Table, 02/09/2010, from Series Math Study Resource.

Hyperlink: www.seriesmathstudy.com/sumreciprocalsoftwotermsquares.htm.

 

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