Question

tính tổng B = 1/20+1/30+1/42+1/65+1/72+1/90

giúp nốt ạ:3

Answer 1

\(B=\dfrac{1}{20}+\dfrac{1}{30}+\dfrac{1}{42}+\dfrac{1}{56}+\dfrac{1}{72}+\dfrac{1}{90}\\ =\dfrac{1}{4\times5}+\dfrac{1}{5\times6}+\dfrac{1}{6\times7}+\dfrac{1}{7\times8}+\dfrac{1}{8\times9}+\dfrac{1}{9\times10}\\ =\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{10}\\ =\dfrac{1}{4}-\dfrac{1}{10}\\ =\dfrac{10}{40}-\dfrac{4}{40}\\ =\dfrac{6}{40}\\ =\dfrac{3}{20}\)