  Recently, Mneimneh proved the remarkable identity \begin{align*} \sum_{k=0}^n
H_k\binom{n}{k} p^k(1-p)^{n-k}=\sum_{i=1}^n \frac{1-(1-p)^i}{i}\quad (p\in
[0,1]) \end{align*} as the main result of a 2023 \emph{Discrete Mathematics}
paper, where $H_k:=\sum\nolimits_{i=1}^k 1/i$ is the classical $k$-th harmonic
number. Thereafter, Campbell provided several other proofs of Mneimneh's
formula as above in a note published in \emph{Discrete Mathematics} in 2023.
Moreover, Campbell also considered how Mneimneh's identity may be proved and
generalized using the \emph{Mathematica package Sigma}. In particular, he found
the generalized Mneimneh's identity \begin{align*} \sum_{k=0}^n x^k y^{n-k}
\binom{n}{k}H_k =(x+y)^n \left(H_n-\sum_{i=1}^n \frac{y^i
(x+y)^{-i}}{i}\right). \end{align*} In this paper, we will prove a more
generalization of Mneimneh's identity involving Bell numbers and some
Mneimneh-type identities involving (alternating) harmonic numbers by using a
few results of our previous papers.
