How to solve Ramanujan's problem by numerical method 2

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How to solve Ramanujan's problem by numerical method 2

  1. 1. How to solve Ramanujan's problem by numerical method and We need to find I0 I0 = 1 1 2 1 3 1 4 1 ...    Define that; I1 = 1 1 3 1 4 1 5 1 ...    And; I2 = 1 1 4 1 5 1 6 1 ...    In the general case; In = 1 1 n 2( ) I n 1  Or; In+1 = 1 I n  n 2( ) I n  Notice I0 that 0 < I0 < 1 So, We need to find the condition of Ik+1 in the Programming1 when k is the large number Initial Condition for Programming k 9999 Programming 1; Assume I0 = 0.5 FindValue1 k( ) I 0 0.5 I n 1 1 I n  n 2( ) I n   n 0 kfor I  I FindValue1 k( ) 0 0 1 2 3 4 5 0.5 0.5 0.333 0.5 0.2 ...  So that; I k 1 0.01 We can approximate that; I k 1 0 Programming 2; FindValue2 k( ) I k 1 0 I n 1 1 n 2( ) I n 1   n k 0for I  I FindValue2 k( ) 0 0 1 2 3 4 5 0.525 0.452 0.404 0.369 0.342 ...  So that, the finally; I 0 0.52513527616098121

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