Four bricks are to be stacked at the edge of a table, each brick overhanging the

Question

Four bricks are to be stacked at the edge of a table, each brick overhanging the one below it, so that the top brick extends as far as possible beyond the edge of the table (Figure 1) A builder wants to construct a corbeled arch (see part (b) of the figure) based on the principle of stability discussed in previous parts of the problem. What minimum number of bricks, each 0.30 m long, is needed if the arch is to span 1.1 m? Be sure to include in the total number of bricks one brick on top and one brick at the base of each half-span of the arch. Express your answer as an integer.

Explanation / Answer

The overhang for each brick, as a fraction of the length, is
x = 1/(2n)
where n is the level from the top.

Each half of the arch spans 1.1 m / 2 = 0.550 m
Then
0.30m * (1/2 + 1/4 + 1/6 + 1/8 + ...) = 0.550 m
1/2 + 1/4 + 1/6 + 1/8 + ... = 1.833

When I go out to 1/(2*20), I get 1.799
and when I go to 1/(2*21), I get 1.823

and when I go to 1/(2*22), I get 1.845

so I conclude we need 2*22 (for the two sides) plus the two base bricks plus the top brick for a total of 47 bricks.
The answer certainly must be an odd number.

Reference: http://www.wolframalpha.com/input/?i=sum(1%2F(2*n))+for+n+from+1+to+22

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