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Homework Statement
Show that if [tex]\vartheta[/tex] is any constant not equal to 0 or a multiple of 2[tex]\pi[/tex], and if u[tex]_{0}[/tex], u[tex]_{1}[/tex], u[tex]_{2}[/tex] is a series that converges monotonically to 0, then the series [tex]\sum u_{n} cos(n\vartheta +a)[/tex] is also convergent, where a is an arbitrary constant.
Homework Equations
The Attempt at a Solution
I have attempted to show convergence via Cauchy's root test, Dirichlet's test, and Abel's test. All 3 of these attempts were unsucessful as one or more conditions required for the tests was not met.