Question

The sum of the reciprocals of the first four consecutive positive integers is greater than two. What is the least number of consecutive positive integers necessary to make the sum of the reciprocals greater than three?

Answer 1

The least number of consecutive positive integer that is required to make the sum of the reciprocals greater than three is 7.

What is an integer?

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.

Learn more about reciprocals at:
brainly.com/question/673545

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