For what values of x do $sum_n=1^infty frac(-1)^n-1cos(nx)n$ and $sum_n=1^infty frac(-1)^n-1sin(nx)n$ converge?
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Is there a way to determine the values of x for which $$sum_n=1^infty frac(-1)^n-1cos(nx)n$$ and $$sum_n=1^infty frac(-1)^n-1sin(nx)n$$ converge? I could not come up with an answer myself and found no other mention of series like these.
sequences-and-series analysis
asked Aug 23 at 1:25
Alex Carlson
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Is there a way to determine the values of x for which $$sum_n=1^infty frac(-1)^n-1cos(nx)n$$ and $$sum_n=1^infty frac(-1)^n-1sin(nx)n$$ converge? I could not come up with an answer myself and found no other mention of series like these.
sequences-and-series analysis
asked Aug 23 at 1:25
Alex Carlson
1
Do you know Dirichlet's test? Try to write sine and cosine using exponentials.
– 4-ier
Aug 23 at 1:44
add a comment |Â
up vote
0
down vote
favorite
up vote
0
down vote
favorite
Is there a way to determine the values of x for which $$sum_n=1^infty frac(-1)^n-1cos(nx)n$$ and $$sum_n=1^infty frac(-1)^n-1sin(nx)n$$ converge? I could not come up with an answer myself and found no other mention of series like these.
sequences-and-series analysis
asked Aug 23 at 1:25
Alex Carlson
1
Is there a way to determine the values of x for which $$sum_n=1^infty frac(-1)^n-1cos(nx)n$$ and $$sum_n=1^infty frac(-1)^n-1sin(nx)n$$ converge? I could not come up with an answer myself and found no other mention of series like these.
sequences-and-series analysis
asked Aug 23 at 1:25
Alex Carlson
1
asked Aug 23 at 1:25
Alex Carlson
1
asked Aug 23 at 1:25
Alex Carlson
1
asked Aug 23 at 1:25
Alex Carlson
1
1
Do you know Dirichlet's test? Try to write sine and cosine using exponentials.
– 4-ier
Aug 23 at 1:44
add a comment |Â
Do you know Dirichlet's test? Try to write sine and cosine using exponentials.
– 4-ier
Aug 23 at 1:44
Do you know Dirichlet's test? Try to write sine and cosine using exponentials.
– 4-ier
Aug 23 at 1:44
Do you know Dirichlet's test? Try to write sine and cosine using exponentials.
– 4-ier
Aug 23 at 1:44
add a comment |Â
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Do you know Dirichlet's test? Try to write sine and cosine using exponentials.
– 4-ier
Aug 23 at 1:44