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If S is the sum of reciprocals of a list of consecutive integers from 45 to 54, inclusive, S is approximately equal to
  • a)
    0.1
  • b)
    0.2
  • c)
    0.3
  • d)
    0.4
  • e)
    0.5
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
If S is the sum of reciprocals of a list of consecutive integers from ...
Calculation of S:
To find the sum of reciprocals of the consecutive integers from 45 to 54, we need to calculate the reciprocals of each of these integers first.

Reciprocals of the integers:
1/45, 1/46, 1/47, 1/48, 1/49, 1/50, 1/51, 1/52, 1/53, 1/54

Calculating the sum:
S = 1/45 + 1/46 + 1/47 + 1/48 + 1/49 + 1/50 + 1/51 + 1/52 + 1/53 + 1/54

Approximating S:
Approximating each of the reciprocals to the nearest tenths place:
1/45 ≈ 0.022
1/46 ≈ 0.022
1/47 ≈ 0.021
1/48 ≈ 0.021
1/49 ≈ 0.020
1/50 = 0.02
1/51 ≈ 0.020
1/52 = 0.019
1/53 ≈ 0.019
1/54 ≈ 0.018
Summing up these approximations:
S ≈ 0.022 + 0.022 + 0.021 + 0.021 + 0.020 + 0.02 + 0.020 + 0.019 + 0.019 + 0.018
S ≈ 0.202
Therefore, the sum S of the reciprocals of the consecutive integers from 45 to 54 is approximately equal to 0.2, which corresponds to option (b).
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If S is the sum of reciprocals of a list of consecutive integers from 45 to 54, inclusive, S is approximately equal toa)0.1b)0.2c)0.3d)0.4e)0.5Correct answer is option 'B'. Can you explain this answer?
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