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Mathematics
Problem
Given that
∑
n
=
1
∞
1
2
n
=
1
\sum_{n=1}^{\infty}\dfrac{1}{2^{n}}=1
∑
n
=
1
∞
2
n
1
=
1
, determine the sum of the series
1
2
10
+
1
2
9
+
⋯
+
1
2
1
\tfrac1{2^{10}}+\tfrac1{2^{9}}+\cdots+\tfrac1{2^{1}}
2
10
1
+
2
9
1
+
⋯
+
2
1
1
followed by the remaining terms written in the same decreasing-exponent order. Justify your numerical answer.
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