Proving that a series is not convergent to 1.











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I know that this is the easy stuff, but I'm at the beginning. In the book from where I took this exercise, the answer implies replacing $n$ with $2k$, respectively $2k+1,$ which I think has to do with parity and imparity. In the first case, the limit tends to $1$, and to $-1$ in the second. So the series is not convergent to $1$, which is fine, i knew how to reach this point. Problem is, how did it get to 1 and $-1$? Couldn't really find anything $pi$-related to confirm that somehow $2pi$ multiplied with any number inside $cos$ is equal to $cos(2pi)$, so I'm not sure. I would appreciate a more detailed answer, if you don't mind.






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  • What series are you talking about?
    – Arthur
    1 hour ago






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    You have not described a problem. All you did was talk about some secret problem.
    – William Elliot
    53 mins ago















up vote
-3
down vote

favorite












I know that this is the easy stuff, but I'm at the beginning. In the book from where I took this exercise, the answer implies replacing $n$ with $2k$, respectively $2k+1,$ which I think has to do with parity and imparity. In the first case, the limit tends to $1$, and to $-1$ in the second. So the series is not convergent to $1$, which is fine, i knew how to reach this point. Problem is, how did it get to 1 and $-1$? Couldn't really find anything $pi$-related to confirm that somehow $2pi$ multiplied with any number inside $cos$ is equal to $cos(2pi)$, so I'm not sure. I would appreciate a more detailed answer, if you don't mind.






real-analysis







share|cite|improve this question









New contributor




Iustin Theodor is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
















  • 1




    Welcome to MSE. Please read this text about how to ask a good question.
    – José Carlos Santos
    2 hours ago










  • What series are you talking about?
    – Arthur
    1 hour ago






  • 1




    You have not described a problem. All you did was talk about some secret problem.
    – William Elliot
    53 mins ago













up vote
-3
down vote

favorite









up vote
-3
down vote

favorite











I know that this is the easy stuff, but I'm at the beginning. In the book from where I took this exercise, the answer implies replacing $n$ with $2k$, respectively $2k+1,$ which I think has to do with parity and imparity. In the first case, the limit tends to $1$, and to $-1$ in the second. So the series is not convergent to $1$, which is fine, i knew how to reach this point. Problem is, how did it get to 1 and $-1$? Couldn't really find anything $pi$-related to confirm that somehow $2pi$ multiplied with any number inside $cos$ is equal to $cos(2pi)$, so I'm not sure. I would appreciate a more detailed answer, if you don't mind.






real-analysis







share|cite|improve this question









New contributor




Iustin Theodor is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.











I know that this is the easy stuff, but I'm at the beginning. In the book from where I took this exercise, the answer implies replacing $n$ with $2k$, respectively $2k+1,$ which I think has to do with parity and imparity. In the first case, the limit tends to $1$, and to $-1$ in the second. So the series is not convergent to $1$, which is fine, i knew how to reach this point. Problem is, how did it get to 1 and $-1$? Couldn't really find anything $pi$-related to confirm that somehow $2pi$ multiplied with any number inside $cos$ is equal to $cos(2pi)$, so I'm not sure. I would appreciate a more detailed answer, if you don't mind.






real-analysis




real-analysis






share|cite|improve this question









New contributor




Iustin Theodor is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.











share|cite|improve this question









New contributor




Iustin Theodor is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.









share|cite|improve this question




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edited 2 hours ago









Gaby Boy Analysis

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Iustin Theodor is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.






Iustin Theodor is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.








  • 1




    Welcome to MSE. Please read this text about how to ask a good question.
    – José Carlos Santos
    2 hours ago










  • What series are you talking about?
    – Arthur
    1 hour ago






  • 1




    You have not described a problem. All you did was talk about some secret problem.
    – William Elliot
    53 mins ago














  • 1




    Welcome to MSE. Please read this text about how to ask a good question.
    – José Carlos Santos
    2 hours ago










  • What series are you talking about?
    – Arthur
    1 hour ago






  • 1




    You have not described a problem. All you did was talk about some secret problem.
    – William Elliot
    53 mins ago








1




1




Welcome to MSE. Please read this text about how to ask a good question.
– José Carlos Santos
2 hours ago




Welcome to MSE. Please read this text about how to ask a good question.
– José Carlos Santos
2 hours ago












What series are you talking about?
– Arthur
1 hour ago




What series are you talking about?
– Arthur
1 hour ago




1




1




You have not described a problem. All you did was talk about some secret problem.
– William Elliot
53 mins ago




You have not described a problem. All you did was talk about some secret problem.
– William Elliot
53 mins ago















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