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Old 2010-01-28, 06:52   #1
Joshua2
 
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Default 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!
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Old 2010-01-28, 09:35   #2
fivemack
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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.
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Old 2010-01-28, 09:47   #3
Joshua2
 
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Quote:
Originally Posted by fivemack View Post
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
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Old 2010-01-28, 10:29   #4
wblipp
 
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Quote:
Originally Posted by Joshua2 View Post
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?
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Old 2010-01-28, 22:10   #5
Joshua2
 
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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
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Old 2010-01-28, 22:13   #6
Joshua2
 
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Here is the picture of the problem...
Attached Thumbnails
Click image for larger version

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Old 2010-01-28, 23:36   #7
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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.
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Old 2010-01-28, 23:42   #8
wblipp
 
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Quote:
Originally Posted by Joshua2 View Post
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.
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Old 2010-01-29, 01:25   #9
Joshua2
 
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i got it! now i'm doing a similar one with fibinochhi numbers
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Old 2010-01-29, 08:23   #10
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Quote:
Originally Posted by Joshua2 View Post
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
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Old 2010-01-29, 10:35   #11
Joshua2
 
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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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