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 2010-01-28, 06:52 #1 Joshua2     Sep 2004 13×41 Posts can anyone here do algebra :) apparently I can't lol. I'm trying to do a proof by induction and I think I'm getting tripped up on the algebra. so prove some of harmonic series is = (n+1) * harmonic nth term - n so 1 = 2*1-1 now for tricky part (n+1) Hn - n + Hn+1 = (n+2)Hn+1 - (n+1) where Hn is nth harmonic term so I think this reduces to (n+1)/n - n + 1/(n+1) = (n+2)/(n+1) - (n+1) 1 + 1/n - n + 1/(n+1) = (n+2)/(n+1) - n - 1 (2n+1) / (n*(n+1)) + 1 =... I tried going farther but didn't get anywhere... Thanks guys!
 2010-01-28, 09:35 #2 fivemack (loop (#_fork))     Feb 2006 Cambridge, England 142628 Posts You're not writing down clearly what you're trying to prove, which is always a bad start. Let A = 1+1/2+1/3+1/4 = 25/12 Let B = 1+1/2+1/3+1/4+1/5 = 137/60 and you seem to be wanting to prove that B = 5A-4, which is not the case.
2010-01-28, 09:47   #3
Joshua2

Sep 2004

13·41 Posts

Quote:
 Originally Posted by fivemack You're not writing down clearly what you're trying to prove, which is always a bad start. Let A = 1+1/2+1/3+1/4 = 25/12 Let B = 1+1/2+1/3+1/4+1/5 = 137/60 and you seem to be wanting to prove that B = 5A-4, which is not the case.
I'm trying to prove that the sum of the harmonic series, (I'm assuming 1+1/2+1/3+1/4...+1/n) = (n+1) * harmonic nth term - n
I'm sorry I can't state it any better.

Last fiddled with by Joshua2 on 2010-01-28 at 09:50

2010-01-28, 10:29   #4
wblipp

"William"
May 2003
New Haven

22×32×5×13 Posts

Quote:
 Originally Posted by Joshua2 I'm trying to prove that the sum of the harmonic series, (I'm assuming 1+1/2+1/3+1/4...+1/n) = (n+1) * harmonic nth term - n I'm sorry I can't state it any better.
Let's follow fivemack's lead and show what you are trying to prove for n=5. It looks you want to prove

(1+1/2+1/3+1/4+1/5)=6*(1/4)-5

or, depending on the meaning of "harmonic nth term"

(1+1/2+1/3+1/4+1/5)=6*(1/5)-5

or possibly

(1+1/2+1/3+1/4+1/5)=6*(25/12)-5

Which one is it?

 2010-01-28, 22:10 #5 Joshua2     Sep 2004 10000101012 Posts Thanks guys, it appears none are true plugging into a calculator. So I made a mistake somewhere before? I found out that H sub 4 is 25/12 Last fiddled with by Joshua2 on 2010-01-28 at 22:15
 2010-01-28, 22:13 #6 Joshua2     Sep 2004 13·41 Posts Here is the picture of the problem... Attached Thumbnails
 2010-01-28, 23:36 #7 axn     Jun 2003 23·19·31 Posts This is correct. Here Hn is _not_ the harmonic n-th term, it is the sum of the harmonic series upto the n-th term.
2010-01-28, 23:42   #8
wblipp

"William"
May 2003
New Haven

22·32·5·13 Posts

Quote:
 Originally Posted by Joshua2 Here is the picture of the problem...
Hi is the partial sum.

H1 = 1
H2 = 3/2
H3 = 11/6
H4 = 25/12
H5 = 137/60

For n=5 you want to show
1 + 3/2 + 11/6 + 25/12 + 137/60 = 6*(137/60) - 5

This is true, at least for n=5, so there is a hope of finishing the proof.

This is the Homework Help forum, so I think we've done our help by clarifying the problem statement - it's time for you to try some more. If you need more help, please come back with a summary of what you've tried and where you are stuck.

 2010-01-29, 01:25 #9 Joshua2     Sep 2004 13×41 Posts i got it! now i'm doing a similar one with fibinochhi numbers
2010-01-29, 08:23   #10
flouran

Dec 2008

2×5×83 Posts

Quote:
 Originally Posted by Joshua2 i got it! now i'm doing a similar one with fibinochhi numbers
Never heard of "fibinochhi" numbers before, but I have heard of Fibonacci numbers

Last fiddled with by flouran on 2010-01-29 at 08:23

 2010-01-29, 10:35 #11 Joshua2     Sep 2004 10000101012 Posts yah i knew my chance of spelling it right was low, but I got it down anyway. My spelling is bad after midnight.

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