No, Prasenjeet, we cannot lump alkanes, alkynes and alkenes into one "homologous" series.
The general formula for an alkane is C_{n}H_{2n + 2} (n ≥ 1) in which the repeating unit is CH_{2}
For 1alkenes the general formula is C_{n}H_{2n} (n ≥ 2) for which the repeating unit is also CH_{2}, but notice how the general formula differs from that of alkanes.
As a final example consider 1alkynes for which the general formula is C_{n}H_{2n} − 2 (n ≥ 2).
Compounds form a homologous series as long as they have the same general formula. Thus methane, ethane, propane, butane etc. form one homologous series (the alkanes). Alkenes and alkynes form their own series.
1/20/2014

William S.