Answer

问题及解答

设 $f(x)=a_1\sin x+a_2\sin 2x+\cdots+a_n\sin nx$, 且 $|f(x)|\leqslant |\sin x|$, 证明: $|a_1+2a_2+\cdots+na_n|\leqslant 1$.

Posted by haifeng on 2022-10-01 23:25:15 last update 2022-10-01 23:25:15 | Edit | Answers (0)

设 $f(x)=a_1\sin x+a_2\sin 2x+\cdots+a_n\sin nx$, 且 $|f(x)|\leqslant |\sin x|$, 证明:

\[|a_1+2a_2+\cdots+na_n|\leqslant 1.\]