The least number of consecutive positive integer that is required to make the sum of the reciprocals greater than three is 7.
An integer is simply a number that is not a fraction.
The first four consecutive positive integers are:
1, 2, 3 , 4.
Their reciprocals are:
1/1, 1/2, 1/3, 1/4; and
The sum of them are greater than 2; that is
1/1 + 1/2 + 1/3 + 1/4 = 2.08333333333 > 2
to make the expression >3
We would require the following integers
1/1 + 1/2 + 1/3 + 1/4+ (1/5) + (1/6) + (1/7) + (1/8)+ (1/9) + (1/10) + (1/11) = 3.01987734488
Thus, the additional consecutive reciprocal integers that is required to make the sum of the reciprocal of the fist four greater than 3 is 7.
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