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.

Guest May 27, 2017

#2**+1 **

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.

Guest May 27, 2017