Final answer:
To express the given expression as a simple fraction in lowest terms, we find a common denominator, add the fractions, and simplify the resulting fraction to the lowest terms. The answer of the given expression is 5/6.
Step-by-step explanation:
To express the given expression as a simple fraction in lowest terms, we need to find a common denominator for all the fractions and then add them together. The denominators of the fractions are 1*2, 2*3, 3*4, 4*5, and 5*6 respectively. The least common multiple of these denominators is 60. Therefore, the expression can be rewritten as:
1/2 + 1/6 + 1/12 + 1/20 + 1/30
Now, we can add these fractions together. The common denominator is 60, so we multiply each fraction by the appropriate factor to convert the denominator to 60:
30/60 + 10/60 + 5/60 + 3/60 + 2/60
Adding these fractions together gives us:
50/60
Finally, we can simplify this fraction by dividing both the numerator and denominator by their greatest common divisor, which is 10. This gives us the final answer: 5/6