Let $\displaystyle f( a) ={ 101 }^{ a }-101{ (100) }^{ a }+\frac { 101\times 100 }{ 2 } { (99) }^{ a }-\frac { 101\times 100\times 99 }{ 6 } { (98) }^{ a } \dots .$

If $\displaystyle A=\left\{ a : a \in \mathbb{N} | f(a) = 0 \right\},$

find $\displaystyle \sum _{ a\in A } a$