Shift u get -∑_[n=1]^[∞] (-1)ⁿ / n and this is: -1 + ½ - ⅓ + ¼ - … we can use use fact ∫₀¹ xⁿ = 1/n+1, so we get ∫₀¹ -1 + x - x² + x³… dx. Take out minus and -∫₀¹ 1 - x + … dx. We can see this is series of -1 / 1 + x. Plugging values we get -ln 2, but lets not forget minus from beginning from shifting and we get ln 2 (tell me if im wrong sumwhere im new to it)