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Algebra 2SuperchallengeRational Expressions & Functions

Rational Expressions & Functions · Superchallenge problem

Find the sum of all real solutions of

1x(x+1)+1(x+1)(x+2)+1(x+2)(x+3)+⋯+1(x+9)(x+10)=1011.\dfrac{1}{x(x + 1)} + \dfrac{1}{(x + 1)(x + 2)} + \dfrac{1}{(x + 2)(x + 3)} + \cdots + \dfrac{1}{(x + 9)(x + 10)} = \dfrac{10}{11}.