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last digit of denominator of product k/ 2^k (Chile 2016 L1 L2 P4)
last digit of denominator of product k/ 2^k (Chile 2016 L1 L2 P4)
Source:
October 22, 2022
algebra
Problem Statement
The product
1
2
⋅
2
4
⋅
3
8
⋅
4
16
⋅
.
.
.
⋅
99
2
99
⋅
100
2
100
\frac12 \cdot \frac24 \cdot \frac38 \cdot \frac{4}{16} \cdot ... \cdot \frac{99}{2^{99}} \cdot \frac{100}{2^{100}}
2
1
⋅
4
2
⋅
8
3
⋅
16
4
⋅
...
⋅
2
99
99
⋅
2
100
100
is written in its most simplified form. What is the last digit of the denominator?
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