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 \( \displaystyle \sum _{ a\in A } a \)

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