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2024-09-13 06:01:53
\(B=\dfrac{1}{9.10}-\dfrac{1}{8.9}-\dfrac{1}{7.8}-...-\dfrac{1}{2.3}-\dfrac{1}{1.2}\)
\(B=\dfrac{1}{9.10}-\left(\dfrac{1}{1.2}+\dfrac{1}{2.3}+...+\dfrac{1}{7.8}+\dfrac{1}{8.9}\right)\)
\(B=\dfrac{1}{90}-\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{7}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{9}\right)\)
\(B=\dfrac{1}{90}-\left(1-\dfrac{1}{9}\right)\)
\(B=\dfrac{1}{90}-\left(\dfrac{9}{9}-\dfrac{1}{9}\right)\)
\(B=\dfrac{1}{90}-\dfrac{8}{9}\)
\(B=\dfrac{1}{90}-\dfrac{80}{90}\)
\(B=\dfrac{-79}{90}\)