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The intersection of the image with positive integer y = (- K / K + 1) x + (1 / K + 1) K and X, Y axes is a, B, and the origin is o. let the AOB area of RT triangle be SK, and find S1 + S2 + What is the value of s2009?
In addition, x = 0 → y = 1 / [(K + 1) k]; y = 0 → x = 1 1s (k) = - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - S2009=（1/2）*（1-1/2+1/2-1/3+…… -1/2008+1/2008-1/2009)=(1/2)*(1-1/2009)=10...
The intersection of the function image of the linear function y = - (K / K + 1) x + 1 / K + 1 (k is a positive integer) and the x-axis, Y-axis is a, B, O as the origin. Let the area of RT △ AOB be sk
Find S1 + S2 +. S1994=________ .
A. The coordinates of two points B are (1 / K, 0), [0,1 / (K + 1)] SK = AO * Bo / 2 = 1 / [2K (K + 1)] S1 + S2 +. S1994 = 1 / 2 [1 / (1 * 2) + 1 / (2 * 3) + 1 / (3 * 4). + 1 / (1994 * 1995)] = 1 / 2 [1-1 / 2 + 1 / 2-1 / 3 + 1 / 3-1 / 4 +. + 1 / 1994-1 / 1995] = 1 / 2 (1-1 / 1995) = 997 / 1995
RELATED INFORMATIONS
- 1. If the intersection of the image of the linear function y = - K / K + 1 x + 1 / K + 1 (k is a natural number) and the x-axis and y-axis is a, B.O. let the area of RT △ ABO be SK, then (1) find S1 (2) find S1 + S2 + S3 + +Value of s2010
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