- #1
Amaelle
- 310
- 54
- Homework Statement
- look at the image
- Relevant Equations
- Sommation
taylor series
That is derailing spectacularly ! Write down a few terms of the one and the other and see that the two are very different !Amaelle said:I started by removing the 4
you are right thank youAmaelle said:Homework Statement:: look at the image
Relevant Equations:: Sommation
taylor series
Greetings!
I want to caluculate the summation of this following serie
View attachment 297263
I started by removing the 4 by
View attachment 297264
and then
View attachment 297265
and I thought of the taylor expansion of
Log(1-x)=-∑x^{n}/n but as the 2 is not inside (-1,1) I couldn´t use it
any hint?
thank you!
Best !
thank you!anuttarasammyak said:If you have already studied calculus, you may make use of the relation
[tex] \int_{-\infty}^1 2^{mt} dt = [\frac{2^{mt}}{m \ln 2}]_{-\infty}^1=\frac{1}{\ln 2}\frac{2^m}{m}[/tex]
for easy summation.
Haha, if you're starting in the wrong direction it won't be solved anywayAmaelle said:the main problem remain unsolved
So the actual homework statement isAmaelle said:Homework Statement:: look at the image
Relevant Equations:: Sommation
taylor series
I want to caluculate
BvU said:Haha, if you're starting in the wrong direction it won't be solved anyway
I don't have all the answers but a modest beginning might come about by writing down a bunch of terms for a low value of ##N## ...Indeed, that was a huge contribution! I can do this kind of deadly mistakes during exams, thanks a million for point it out!
Indeed, my instructor said he can asked it in the exam, so I tried to solved it, :)Fred Wright said:I doubt you will see this problem on an exam. The solution is rather difficult resulting in a complex valued function involving the Lerch transcendent. I'm surprised that it was issued as a homework problem (that's just mean).
Besides convergence of the Taylor series, you're trying to calculate a finite sum whereas the Taylor series is an infinite sum.Amaelle said:I thought of the taylor expansion of
Log(1-x)=-∑x^{n}/n but as the 2 is not inside (-1,1) I couldn´t use it
A partial sequence is a sequence of numbers that is only a portion of a larger sequence. It may be a finite or infinite sequence, but it does not include all the terms of the larger sequence.
Summation is a mathematical operation that involves adding together a sequence of numbers. It is often represented by the symbol ∑ and is used to find the total value of a series of numbers.
To calculate the summation of a partial sequence, you simply add together all the numbers in the sequence. If the sequence is finite, you can do this manually. If the sequence is infinite, you can use a mathematical formula or a computer program to calculate the summation.
The summation of a partial sequence is important because it allows us to find the total value of a sequence of numbers without having to add them individually. It is a useful tool in many areas of mathematics and science, such as in calculating probabilities, finding areas under curves, and solving differential equations.
Yes, the summation of a partial sequence can be negative. This can happen if the sequence contains both positive and negative numbers, and the negative numbers have a greater magnitude than the positive numbers. In this case, the summation would result in a negative value.