Question 375346
<pre>
The sequence of denominators is 

2, 5, 10, 17, 26, 37, ...

and we notice that each term of this sequence is 1 more than the
corresponding term in the sequence of squares:

1, 4, 9, 16, 25, 36, ...

And we know that the formula for the nth term of that sequence is

{{{n^2}}}

So the formula for the nth term of the sequence of denominators 

2, 5 10 17, 26, 37, ...

is {{{n^2+1}}}

Then the formula for the nth term of the sequence of the absolute values 
of the terms of the given sequence,

1/2, 1/5, 1/10, 1/17, 1/26, 1/37

is

{{{1/(n^2+1)}}}

But the signs alternate in the given sequence.  To cause the signs to alternate,
multiply by the "alternating-sign factor" {{{(-1)^(n+1)}}}

So the final answer is

{{{a[n]}}}{{{""=""}}}{{{(-1)^(n+1)/(n^2+1)}}}

Edwin</pre>