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If the sum
∑k=049(−1)k(992k)\sum_{k = 0}^{49} (-1)^k {99 \choose 2k}k=0∑49(−1)k(2k99)
is written in the form aba^bab, where a,ba, ba,b are integers and bbb is as large as possible, what is a+b?a+b?a+b?
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