Wolfram Alpha and Mathematica give an incorrect result (numerically) for the following infinite sum:

N[Sum[((-1)^n)/(n - (-1)^n), {n, 1, Infinity}]]
(* 0.700059 *)

Here's the result on Wolfram Alpha. Why the series isn't correctly evaluated?

Wolfram Alpha and Mathematica give an incorrect result (numerically) for the following infinite sum:

N[Sum[((-1)^n)/(n - (-1)^n), {n, 1, Infinity}]]
(* 0.700059 *)

Here's the result on Wolfram Alpha. Why the series isn't correctly evaluated?
The answer should be $\log(2)$.

Here is a code of an infinite series I proposed, and that is wrongly computed both by
WolframAlpha and Mathematica (numerically I mean).

                     N[Sum[((-1)^n)/(n - (-1)^n), {n, 1, Infinity}]]

Or

WolframAlpha Link that tells us the limit is 0.700059.

  Why the series isn't correctly evaluated?

Wolfram Alpha and Mathematica give an incorrect result (numerically) for the following infinite sum:

N[Sum[((-1)^n)/(n - (-1)^n), {n, 1, Infinity}]]
(* 0.700059 *)

Here's the result on Wolfram Alpha. Why the series isn't correctly evaluated?