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Janaka Rodrigo
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Janaka RodrigoLevel 2
Asked: August 23, 20232023-08-23T16:21:57+05:30 2023-08-23T16:21:57+05:30In: Geometry ( ජ්‍යාමිතිය )

Geometrical approach to evaluate the sum of infinite number of terms of series of angles.

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There was an Olympiad question of  evaluating the sum arccot(2) + arccot(3) by geometrical approach. My issue is how can you use only one figure to evaluate sum of infinite series of angles arccot(3) + arccot(7) + arccot(13)+….and show that equal to π/4 without any description in words.

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  1. Janaka Rodrigo
    Janaka Rodrigo Level 2 English medium advanced level mathematics teacher at St Benedicts College Colombo 13
    2023-08-23T16:33:46+05:30Added an answer on August 23, 2023 at 4:33 pm

    We have plenty of applications related to convergent geometric series but not for this particular case. I believe the method used here can be totally new approach. The most important thing here is I’m using only one figure and basic geometry theorems.  All points named in the figure have integer coordinates but because of practical difficulties I couldn’t draw a perfect figure in GeoGebra.  Here you have the link for more details,

    https://www.geogebra.org/m/j5yvst8s



     

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