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Found problems: 1

ICMC 4, 3
Tags: sin , integration , calculus
Let $\displaystyle s_n=\int_0^1 \text{sin}^n(nx) \,dx$. (a) Prove that $s_n \leq \dfrac 2n$ for all odd $n$. (b) Find all the limit points of the sequence $s_1, s_2, s_3, \dots$. [i]Proposed by Cristi Calin[/i]