Easy If You Know It's Property !

Probability Level 5

Let f(a)=101a101(100)a+101×1002(99)a101×100×996(98)a. \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 A={a:aNf(a)=0},\displaystyle A=\left\{ a : a \in \mathbb{N} | f(a) = 0 \right\},
find aAa \displaystyle \sum _{ a\in A } a

Original
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