Final answer:
To show that the given summation equals 1, we can use a series of steps involving inequalities and re-expressing fractions with the same numerator and denominator resulting in 1.
Step-by-step explanation:
To show that the given summation equals 1, we can use a series of steps. First, let's consider the inequality that says 1/2 is less than 1/3. Therefore, their sum must be less than 1. Now, let's look at the inequality that states 7/10 is larger than 1. So, their sum must be larger than 1 + 1 = 2.
By understanding these inequalities, we can recreate the common denominator scheme. For example, let's take the case of 1/2 + 1. We can bound it between 0.75 and 1. This graphical representation can show us how the denominators (2 and 3) conspire to create the missing gap of 1. By multiplying and re-expressing the fractions, we can add the numerators directly and make the denominators the same. This results in 2/6 + 3/6 = 5/6.
Overall, as long as we perform the same operation on both sides of the equals sign, the expression remains equality. For example, if we have a fraction with the same quantity in the numerator and the denominator, the value will be 1. Therefore, the given summation equals 1.