A right-angled triangle has two equal sides of inch. One of these sides, drawn horizontally, is divided into equal portions. On each portion after the first, a rectangle is formed with height equal to the vertical distance from the left-hand end of the portion to the hypotenuse of the triangle. Find the sum of rectangle areas () and its limiting value.
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A right-angled triangle has two equal sides of 1 inch. One of these sides, drawn horizontally, is divided into (n+1) equal portions. On each portion after the first, a rectangle is formed with height equal to the vertical distance from the left-hand end of the portion to the hypotenuse of the triangle. Find the sum of rectangle areas (S) and its limiting value. (A) S = n/(n+1) and the limit is 1 (B) S = n/(2(n+1)) and the limit is 1/2 (C) S = (n+2)/(n+1) and the limit is 1 (D) S = (n+2)/(2(n+1)) and the limit is 1/2
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This question is on Arithmetic and geometric progressions and special series, part of Sequences, series and convergence in Mathematics.
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Question from the DSE 2021 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.