This paper investigates the properties of the series $a_1+a_2+...+a_n+...$, where $a_{2k-1}=\frac{1}{2^{2k-1}}$, $a_{2k}=\frac{1}{2^{2k}+1}$, which is referred to as the perturbed binary series.
It is shown that for the tails of the series, defined as $r_n=a_{n+1}+a_{n+2}+...$ and for the terms of the series, the inequalities $$a_{2k-1}>r_{2k-1}, \;\;a_{2k}<r_{2k}$$
hold for any $k\in N$. These inequalities ensure that the set $$E(a_n)=\left\{x: x=\sum\limits_{n\in M\subset N}a_n, \; M\in 2^N\right\}$$ of all subsums of the series satisfies the necessary conditions for Cantor-type structure, in particular, nowhere denseness.

Explicit expressions are obtained for the differences $a_n-r_n$, which characterize the lengths of certain intervals adjacent to the set $E$ specifically the intervals of the form $(r_{2k-1};a_{2k-1})$ as well as the overlaps of cylindrical segments
$\Delta_{c_1...c_m}=[u;v]$, where $(c_1,...,c_m)$ is an ordered tuple of zeros and ones,
 $u=c_1a_1+...+c_ma_m$, $v=u+r_m$.

 The asymptotic behavior of the ratio $\frac{r_n-a_n}{r_{n-1}}$, is described; it reflects the progressive “reduction” of overlaps and “gaps” in the corresponding cylindrical segments.

Several other properties of the given series are also established.

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