What is the value of
n=2∑255(log2n)(log2(n+1))log2(1+n1) ?
Answer Choices:
A. 43
B. 1−log22551
C. 87
D. 1615
E. 1
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We can write:
n=2∑255(log2n)(log2(n+1))log2(1+n1)=n=2∑255log2(n)⋅log2(n+1)log2(n+1)−log2(n)=n=2∑255(log2(n)1−log2(n+1)1)=log2(2)1−log2(256)1=1−81=87
by telescoping. Therefore, the answer is (C) 87.
The problems on this page are the property of the MAA's American Mathematics Competitions