## A series involving harmonic numbers

Does anyone know the exact value of this: ∞∑k=1(−1)kHkk or this: ∞∑k=1(−1)kH(2)kk Thanks! Thanks again for the answers! I found very interesting that the integral gives exact values up to r=3 but from 4 this integral gives not exact values: ∫0−1Li4(t)t(1−t)dt because wolfram says that “no results found in terms of standard mathematical functions” Answer … Read more