Signal's Fundamental Frequency is different from Plotted Signal
With $k$ a continuous variable, the frequencies of the sinusoids in the first sum are $f_n=n$, i.e. they are integers. The frequencies in the second sum are integer multiples of $\frac32$. The highest fundamental frequency of which all those frequencies are integer multiples is $f_0=\frac12$. The frequencies in the first sum are given by $2mf_0$ (with integer $m$), and the frequencies in the second sum are $3mf_0$. With a fundamental frequency of $f_0=\frac12$, the fundamental period is $T=2$, as observed by you.