Weird large K symbolTake a look at this symbol: π = 3 + K ∞ k = 1 ( 2 k − 1 ) 2 6 Does it look familiar to you? If so please help me!

Question

Weird large K symbolTake a look at this symbol:  π  =  3  +                                          K                              ∞              k      =      1                  (      2      k      −      1              )        2              6  Does it look familiar to you? If so please help me!

umshikepl · Accepted Answer

It is the notation for a continued fraction. In general:      b    0    +                                          K                              ∞              k      =      1            (                  a        k                    b        k              )    =      b    0    +                                                              a            1                                                                                        b            1                    +                                                                                                                                      a                    2                                                                                                                                                                                        b                    2                                    +                                                                                                                                                                                                              a                            3                                                                                                                                                                                                                                                                                        b                            3                                                    +                                                                                                                                                                                                                                                                                      a                                    4                                                                                                                                                                                                                                                                                                                                                                                        b                                    4                                                                    +                                  ⋱                                                                                                                                                                                                                                                                                                                  Therefore, the continued fraction representation you have written above for   π is:  π  =  3  +                                          K                              ∞              k      =      1                  (      2      k      −      1              )        2              6    =  3  +                                                              1            2                                                                            6          +                                                                                                                                      3                    2                                                                                                                                                                    6                  +                                                                                                                                                                                                              5                            2                                                                                                                                                                                                                                                            6                          +                                                                                                                                                                                                                                                                                      7                                    2                                                                                                                                                                                                                                                                                                                                                    6                                  +                                  ⋱                                                                                                                                                                                                                                                                                                                  A proof of this result can be found on pages 399-401 of this document by Paul Loya.

Weird large K symbol Take a look at this symbol: pi=3+K_(k=1)^(oo)((2k-1)^2)/(6) Does it look familiar to you? If so please help me!

Answered question

Answer & Explanation

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