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22990atinesh
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Can anybody tell me how this is possible
Please check this linkBvU said:It looks to me as if it isn't possible in the first place. Who claims it is ? Any restrictions on n and h ?
I see a common factor n in front and then something on the left that depends on n, whereas the remainder on the right does not depend on n.
Actually I've seen lots of places where they have done itSamy_A said:Formally, it looks like they replace the summation index ##i## by ##j=\lg n-i##, as that would give ##\sum_{j=\lg n-1}^1\frac{1}{j}##. Then they rename the summation index ##i##.
EDIT: sorry, that's for the equality on the first page in the linked pdf, not the equality in post 1. My confusion.
logarithm is base 2HallsofIvy said:Is this supposed to hold for arbitrary "n" and "h"? If so we can check by taking specific values for n and h. If we take, say, n= h= 1, the formula becomes [itex]\frac{2}{log(2)- 0}= \frac{2}{1}[/itex] which clearly is not true unless the logarithm is to be "base 2". Is that the case?
22990atinesh said:Can anybody tell me how this is possible
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Yes, nothing wrong with it.22990atinesh said:Actually I've seen lots of places where they have done it
See the below link at example the guy has done the same thing
http://clrs.skanev.com/04/problems/03.html
There appears to be an error in your equation. I looked up your reference and the upper limit is log(n)-1 not h-1. The equality results from replacing log(n)-i by i. All that does is doing the sum in the opposite direction.22990atinesh said:Can anybody tell me how this is possible
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An approximation of a logarithmic series is a simplified version of the series that uses a finite number of terms to estimate the sum of an infinite series. It is a useful tool for calculating the value of a series without having to add an infinite number of terms.
An approximation of a logarithmic series is calculated using a formula called the Taylor series, which expresses the value of a function as an infinite sum of terms. By truncating the series after a certain number of terms, we can get an estimate of the actual value of the series.
The purpose of approximating a logarithmic series is to simplify complex mathematical calculations. By using a finite number of terms, we can get a close estimate of the actual value of the series without having to perform an infinite number of calculations.
Approximating logarithmic series is commonly used in fields such as physics, engineering, and finance. It can be used to calculate the growth rate of populations, the decay of radioactive substances, and the value of financial investments.
Yes, an approximation of a logarithmic series can be accurate, but it depends on the number of terms used in the approximation. The more terms we include, the closer the approximation will be to the actual value of the series. However, since it is still an estimate, there will always be a margin of error.