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解方程1/x(x+1)+1/(x+1)(x+2)+...+1/(x+8)(x+9)=2x+3/x(x+9)
人气:322 ℃ 时间:2019-10-17 02:55:12
解答
1/x(x+1)+1/(x+1)(x+2)+...+1/(x+8)(x+9)
=(1/x - 1/x+1) + (1/x+1 - 1/x+2) + ...+ (1/x+8 - 1/x+9)
=1/x - 1/x+9
=9/x(x+9) = 2x+3/x(x+9)
所以9 = 2x+3
x=3
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