Solution: Let where are real numbers and where is a positive integer. Given that for all
Chapter 3, Problem 195(choose chapter or problem)
Let \(f(x)=a_{1} \sin x+a_{2} \sin 2 x+\cdots+a_{n} \sin n x\), where \(a_{1}, a_{2}, . . ., a_{n}\) are real numbers and where n is a positive integer. Given that \(|f(x)| \leq|\sin x|\) for all real x, prove
that \(\left|a_{1}+2 a_{2}+\cdots+n a_{n}\right| \leq 1/).
Text Transcription:
f(x)=a_1 sin x+a_2 sin 2x+cdots+a_n sin nx
a_1, a_2, . ., a_n
|f(x)| leq|sin x|
left|a_1+2a_2+cdots+na_n| leq 1
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