Solution
Given:
In this question, we are given that
- "¢ The value of the variable E is determined by adding the reciprocals of the first 10 even natural numbers.
To find:
We need to determine
- "¢ Among the given options, which one can be a possible value of the reciprocal of E.
Approach and Working:
As E equals the sum of the reciprocals of the first 10 even natural numbers, we can write E in the following manner:
- "¢ E = 1/2 + 1/4 + 1/6 + 1/8 + 1/10 + 1/12 + 1/14 + 1/16 + 1/18 + 1/20
Or, E = 1/2 (1 + 1/2 + 1/3 + 1/4 + 1/5 + 1/6 + 1/7 + 1/8 + 1/9 + 1/10)
Now, if we observe the terms within the bracket carefully, we can see that 1 is the largest among all the 10 terms and 1/10 is the smallest among all the 10 terms.
- "¢ If all 10 terms were equal to 1/10, then E would be 1/2 x 10 x 1/10 = 1/2.
- o But since the actual terms are more, we can say that the value of E is greater than 1/2.
"¢ Similarly, if all 10 terms were equal to 1, then E would be 1/2 x 10 x 1 = 5.
- o But since the actual terms are less, we can say that the value of E is less than 5.
Combining the above results, we can say
- "¢ 1/2 < E < 5
Or, 2 > 1/E > 1/5
Or, 2 > 1/E > 0.2
From the given options, only 0.667 falls in the given range.
Hence, the correct answer is option C.
Answer: C