\(B=\dfrac{2}{1.4}+\dfrac{2}{4.7}+\dfrac{2}{7.10}+...+\dfrac{2}{97.100}\)
\(B=\dfrac{2}{3}\left(\dfrac{3}{1.4}+\dfrac{3}{4.7}+\dfrac{3}{7.10}+...+\dfrac{3}{97.100}\right)\)
\(B=\dfrac{2}{3}\left(\dfrac{4-1}{1.4}+\dfrac{7-4}{4.7}+\dfrac{10-7}{7.10}+...+\dfrac{100-97}{97.100}\right)\)
\(B=\dfrac{2}{3}\left(1-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{10}+...+\dfrac{1}{97}-\dfrac{1}{100}\right)\)
\(B=\dfrac{2}{3}\left(1-\dfrac{1}{100}\right)\)
\(B=\dfrac{2}{3}.\dfrac{99}{100}\)
\(B=\dfrac{33}{50}\)
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