1

http://www.mathalino.com/reviewer/algebra/arithmetic-geometric-and-harmonic-progressions

Please go to this link and see how they tell you to find the sum of harmonic prgression. However I am sure it is wrong as

$\frac{1}{a^{-1}+b^{-1}}\neq a+b $

I would like too understand and see the correct formula. Links will do.

P.S I am a ninth grader so don't go too high level math.

N.S.JOHN
  • 1,549
  • I haven't found formula for harmonic sequence sum in the given link.
  • There is no good closed form expression. Even the basic harmonic sequence $\displaystyle a_n=\frac{1}{n}$ as $n=1,2,3,\dots$ has no closed form for its sum (There are some approximations). You might want to read https://www.quora.com/What-is-the-general-formula-for-sum-of-n-terms-of-a-harmonic-progression
    • – Galc127 Feb 08 '16 at 14:03
  • @galc127 scroll down the link page and they show how to find the sum. Their do not give formula. – N.S.JOHN Feb 08 '16 at 14:05
  • I did, they don't show how to find the sum, only how to find each element of the sequence. They do not give formula, because as I have written and zz2Os answered - there is no such formula. – Galc127 Feb 08 '16 at 14:08
  • @galc127 It is clearly written there that the sum of HP will be the reciprocal of the sum of the respective AP. Isn't it wrong? – N.S.JOHN Feb 08 '16 at 14:10
  • It is not written. What's written is that the term of HP will be the reciprocal of the term of AP. I tried to read the part of HP some times as I didn't want to miss anything. I do think you should read again and understand the difference between single term and sum. – Galc127 Feb 08 '16 at 14:12
  • @galc127. Yeah I should get my eyes checked .Got it and thanks for time. – N.S.JOHN Feb 08 '16 at 14:16