MathDB

35

Part of 1984 IMO Longlists

Problems(1)

Finding natural numbers satisfying inequality

Source:

10/9/2010
Prove that there exist distinct natural numbers m1,m2,⋯ ,mkm_1,m_2, \cdots , m_k satisfying the conditions π−1984<25−(1m1+1m2+⋯+1mk)<π−1960\pi^{-1984}<25-\left(\frac{1}{m_1}+\frac{1}{m_2}+\cdots+\frac{1}{m_k}\right)<\pi^{-1960} where π\pi is the ratio between a circle and its diameter.
inequalitiesratioinequalities unsolved