Sum of a Harmonic Progression
Find the sum of the harmonic progression below. Choose the nearest value among the choices.
5 1 + 1 0 1 + 1 5 1 + . . . + 1 0 0 1 + 1 0 5 1
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2 solutions
One way is to find the sum of 5 + 1 0 + 1 5 + 2 0 + 2 5 + 3 0 + 3 5 + 4 0 + 4 5 + 5 0 + 5 5 + 6 0 + 6 5 + 7 0 + 7 5 + 8 0 + 8 5 + 9 0 + 9 5 + 1 0 0 + 1 0 5 = 1 1 5 5 .
Then 1 1 5 5 − 1 = 1 1 5 5 1 = 0 . 0 0 0 8 6 5 8 0 0 8 6 .
Since it's a positive decimal, the nearest answer from the multiple-choice is 0 . 7 .
Therefore the answer is 0 . 7 .
This solution is wrong. Yes it is true that harmonic progression is the reciprocal of arithmetic progression, but it does not mean that it is also the reciprocal of the sum.
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I know that but I am a GCSE student. @Marvin Kalngan
The sum is k = 1 ∑ 2 1 5 k 1 , which we can estimate as 5 1 ∫ 0 . 5 2 0 . 5 x 1 d x = 5 1 ( ln ( 2 0 . 5 ) − ln ( 0 . 5 ) ) ≈ 0 . 7 .