Progressions - Is it G.P. or H.P.?
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I came across the following example yesterday and could not figure it out. Any help is really appreciated.
Find the sum of the following progression from 1st to 1000th term
3, 5/3, 7/5, 9/7, 11/9, ....
sequences-and-series
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up vote
1
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I came across the following example yesterday and could not figure it out. Any help is really appreciated.
Find the sum of the following progression from 1st to 1000th term
3, 5/3, 7/5, 9/7, 11/9, ....
sequences-and-series
Welcome to Mathematics Stack Exchange !! Here we can help you in any kind of mathematical problems, but you have to show what you have tried. Here, the given series is neither in G.P nor in H.P. They are just in form of $(2k+1)/(2k-1)$.
â Anik Bhowmick
Aug 14 at 9:15
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up vote
1
down vote
favorite
up vote
1
down vote
favorite
I came across the following example yesterday and could not figure it out. Any help is really appreciated.
Find the sum of the following progression from 1st to 1000th term
3, 5/3, 7/5, 9/7, 11/9, ....
sequences-and-series
I came across the following example yesterday and could not figure it out. Any help is really appreciated.
Find the sum of the following progression from 1st to 1000th term
3, 5/3, 7/5, 9/7, 11/9, ....
sequences-and-series
asked Aug 14 at 9:11
Prateek West
61
61
Welcome to Mathematics Stack Exchange !! Here we can help you in any kind of mathematical problems, but you have to show what you have tried. Here, the given series is neither in G.P nor in H.P. They are just in form of $(2k+1)/(2k-1)$.
â Anik Bhowmick
Aug 14 at 9:15
add a comment |Â
Welcome to Mathematics Stack Exchange !! Here we can help you in any kind of mathematical problems, but you have to show what you have tried. Here, the given series is neither in G.P nor in H.P. They are just in form of $(2k+1)/(2k-1)$.
â Anik Bhowmick
Aug 14 at 9:15
Welcome to Mathematics Stack Exchange !! Here we can help you in any kind of mathematical problems, but you have to show what you have tried. Here, the given series is neither in G.P nor in H.P. They are just in form of $(2k+1)/(2k-1)$.
â Anik Bhowmick
Aug 14 at 9:15
Welcome to Mathematics Stack Exchange !! Here we can help you in any kind of mathematical problems, but you have to show what you have tried. Here, the given series is neither in G.P nor in H.P. They are just in form of $(2k+1)/(2k-1)$.
â Anik Bhowmick
Aug 14 at 9:15
add a comment |Â
1 Answer
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I have only bad news
$$frac 2k+12k-1=1+frac 22k-1$$
So your sum depends on the harmonic sum of the odds, which depends on a finite sum of the harmonic series itself. No one has a clean closed form formula for this:
$$sum_n=1 ^N frac 1 n $$
Much less this:
$$sum_n=1 ^N frac12 n -1$$
add a comment |Â
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
1
down vote
I have only bad news
$$frac 2k+12k-1=1+frac 22k-1$$
So your sum depends on the harmonic sum of the odds, which depends on a finite sum of the harmonic series itself. No one has a clean closed form formula for this:
$$sum_n=1 ^N frac 1 n $$
Much less this:
$$sum_n=1 ^N frac12 n -1$$
add a comment |Â
up vote
1
down vote
I have only bad news
$$frac 2k+12k-1=1+frac 22k-1$$
So your sum depends on the harmonic sum of the odds, which depends on a finite sum of the harmonic series itself. No one has a clean closed form formula for this:
$$sum_n=1 ^N frac 1 n $$
Much less this:
$$sum_n=1 ^N frac12 n -1$$
add a comment |Â
up vote
1
down vote
up vote
1
down vote
I have only bad news
$$frac 2k+12k-1=1+frac 22k-1$$
So your sum depends on the harmonic sum of the odds, which depends on a finite sum of the harmonic series itself. No one has a clean closed form formula for this:
$$sum_n=1 ^N frac 1 n $$
Much less this:
$$sum_n=1 ^N frac12 n -1$$
I have only bad news
$$frac 2k+12k-1=1+frac 22k-1$$
So your sum depends on the harmonic sum of the odds, which depends on a finite sum of the harmonic series itself. No one has a clean closed form formula for this:
$$sum_n=1 ^N frac 1 n $$
Much less this:
$$sum_n=1 ^N frac12 n -1$$
answered Aug 14 at 9:48
AmateurMathPirate
1,324521
1,324521
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add a comment |Â
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Welcome to Mathematics Stack Exchange !! Here we can help you in any kind of mathematical problems, but you have to show what you have tried. Here, the given series is neither in G.P nor in H.P. They are just in form of $(2k+1)/(2k-1)$.
â Anik Bhowmick
Aug 14 at 9:15