Let's make the signs alternate

Algebra Level 2

What number goes into the blank below?

1+12+14+18+116+=(112+1418+116)×_______{\color{#3D99F6}1} + {\color{#D61F06}\dfrac12} + {\color{#3D99F6}\dfrac14} + {\color{#D61F06}\dfrac18} + {\color{#3D99F6}\dfrac1{16}} + \cdots =\left({\color{#3D99F6}1} - {\color{#D61F06}\dfrac12} + {\color{#3D99F6}\dfrac14} - {\color{#D61F06}\dfrac18} + {\color{#3D99F6}\dfrac1{16}} - \cdots \right) \times \text{\_\_\_\_\_\_\_}

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