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1
Sum floor 2^k/3 from k=0 to 100
Sum floor 2^k/3 from k=0 to 100
Source: All-Russian MO 2000
December 30, 2012
floor function
algebra unsolved
algebra
Problem Statement
Evaluate the sum
⌊
2
0
3
⌋
+
⌊
2
1
3
⌋
+
⌊
2
2
3
⌋
+
⋯
+
⌊
2
1000
3
⌋
.
\left\lfloor \frac{2^0}{3} \right\rfloor + \left\lfloor \frac{2^1}{3} \right\rfloor + \left\lfloor \frac{2^2}{3} \right\rfloor + \cdots + \left\lfloor \frac{2^{1000}}{3} \right\rfloor.
⌊
3
2
0
⌋
+
⌊
3
2
1
⌋
+
⌊
3
2
2
⌋
+
⋯
+
⌊
3
2
1000
⌋
.
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