Is this language LL(1) parseable?
Kurki-Suonio has shown some helpful properties [1]:


  Theorem 1
  Each LL(k) grammar is unambiguous.


That means any inherently ambiguous language is not LL(1).


  Theorem 9
  For any $k&gt;1$ the grammar $G$:
  
  $\qquad \begin{align}
  S &amp;\to aSA \mid \varepsilon \\
  A &amp;\to a^{k - 1} b S \mid c
\end{align}$
  
  generates an LL(k) language which is no LL(k-1) language.


There you have another concrete example by setting $k=2$.



As for your language $L$, assume $L$ is LL(1) and consider the language

$\qquad \displaystyle L' = \{ a^nb^m \mid n &lt; m \land m &gt; 0 \}$.

We make the following observations:


$L'$ is LL(1) by the grammar 

$\qquad \begin{align}
    S &amp;\to AbB \\
    A &amp;\to aAb \mid \varepsilon \\
    B &amp;\to bB \mid \varepsilon
  \end{align}$
Neither $L$ nor $L'$ is regular (by Pumping Lemma).
$L \cap L' = \emptyset$.
$L \cup L' = \{a^nb^m \mid n,m \in \mathbb{N}\} \in \mathsf{REG}$.


In unison, these facts contradict this theorem [2]:


  Theorem 9
  If the finite union of disjoint LL(k) languages is regular, then all the languages are regular.


Thus, $L$ can not be LL(1) (and in fact not LL(k) for any k).




Notes on top-down languages by R. Kurki-Suonio (1969)
Properties of deterministic top-down grammars by D.J. Rosenkrantz and R.E. Stearns (1970)