We evaluate in closed form series of the type ∑u(n)R(n)∑u(n)R(n), with (u(n))n(u(n))n a strongly BB-multiplicative sequence and R(n)R(n) a (well-chosen) rational function. A typical example is: ∑n≥1(−1)s2(n)4n+12n(2n+1)(2n+2)=−14 ∑n≥1(−1)s2(n)4n+12n(2n+1)(2n+2)=−14 where s2(n)s2(n) is the sum of the binary digits of the integer nn. Furthermore closed formulas for series involving automatic sequences that are not strongly BB-multiplicative, such as the regular paperfolding and Golay-Shapiro-Rudin sequences, are obtained; for example, for integer d≥0d≥0: ∑n≥0v(n)(n+1)2d+1=π2d+1|E2d|(22d+2−2)(2d)! ∑n≥0v(n)(n+1)2d+1=π2d+1|E2d|(22d+2−2)(2d)! where (v(n))n(v(n))n is the ±1±1 regular paperfolding sequence and E2dE2d is an Euler number.