Some Infinite Series of Fibonacci Numbers

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  • Katayama Shin-ichi
    Department of Mathematical and Natural Sciences,Faculty of Integrated Arts and Sciences,The University of Tokushima

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In his paper [1],J.G.Goggins has shown a simple formula which relates πand Fibonacci numbers. In this note，we shall prove a generalized formula (4) with some integer parameter k. Then Goggins's formula can be regarded as the special case k = 1 of our new formula (4).

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