# Simple Series

Calculus Level 3

For sequence $\left\{ { a }_{ n } \right\}$, the following holds: ${ a }_{ 1 }=5$ and ${ a }_{ 100 }=200$. Evaluate $\sum _{ k=1 }^{ 99 }{ { a }_{ k } } -\sum _{ k=1 }^{ 50 }{ { a }_{ 2k } } -\sum _{ k=1 }^{ 49 }{ { a }_{ 2k+1 } }$

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