jackleyt said:Homework Statement
The sum of the reciprocals of two consecutive odd integers is 28/195. Find the two integers.
Homework Equations
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The Attempt at a Solution
28/195= 1/x + 1/(x-2)
Solved using quadratic formula and got 3.44, which does not seem to be right.. Any help?
The sum of reciprocals of integers can be calculated by adding the reciprocals of each integer in the given set. For example, if the set is {1,2,3,4}, the sum of reciprocals would be 1/1 + 1/2 + 1/3 + 1/4 = 2.0833.
The formula for finding the sum of reciprocals of integers is 1/1 + 1/2 + 1/3 + ... + 1/n, where n is the number of integers in the given set.
No, the sum of reciprocals of integers cannot be negative. The reciprocals of positive integers will always be positive, and adding positive numbers will result in a positive sum.
Finding the sum of reciprocals of integers is important in various mathematical concepts such as series and sequences, numerical integration, and harmonic mean. It also has applications in physics and engineering.
Yes, there is a pattern in the sum of reciprocals of integers known as the Harmonic Series. As the number of integers in the set increases, the sum approaches a limit, which is known as the harmonic constant and has a value of approximately 0.5772.