# Why is this infinite series wrongly computed by Mathematica?

Could you let me know if Mathematica (newer versions) is able to correctly compute this one?

Sum[(-1)^(n + 1) Cos[3^n x]^3/3^n, {n, 1, Infinity}]

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MMA 9.0.1 gives me -3Cos[x]/4 - is that what you expect? So does WolframAlpha wolfr.am/1hdQ8OK –  blochwave Jun 5 at 8:50
@blochwave this is completely wrong. Wolfram|Alpha does the same mistake. Check it and convince yourself. –  Chris's sis Jun 5 at 8:53
Ok, so is -3Cos[x]/4 the same answer you get in MMA 8.0? –  blochwave Jun 5 at 9:03
@blochwave yes, but this is wrong. –  Chris's sis Jun 5 at 9:05
As a workaround, Assuming[Element[x, Reals], Limit[Sum[(-1)^(n + 1) Cos[3^n x]^3/3^n, {n, 1, m}], m -> Infinity]] gives the correct result. –  Bob Hanlon Jun 5 at 14:22