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Please give the next three terms of this sequence and the method or formula used to calculate them, if possible.   1,  15/8,  21/5,  85/16,  341/35.......
Thank you for any help. 

 May 27, 2017
 #1
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I don't think that is even a sequence.

 May 27, 2017
 #2
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The sequence continues as : 1, 15/8, 21/5, 85/16, 341/35, 1365/128, 5461/315, 4369/256, 1387/55, 69905/3072..........etc.
The easiest way to see a pattern in such a sequences is to look at the numerator(the top number) and the denominator(the bottom number) separately. If you do that, you will see that the numerator seems to use this formula: (2^(2n) - 1), and the denominator seems to use this formula: (n + 2)!!. !! is called "the double factorial function". Example: 10!! =10 x 8 x 6 x 4 x 2 =3,840. 0!! is defined as 1.
So, your formula appears to be: (2^(2n) - 1) / (n + 2)!!, which is the genarating function.
Notice that the improper fractions are all reduced to their absolute minimum.

 May 27, 2017

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