bài 1 :tìm x biết
\(\dfrac{1}{2.3}\)+\(\dfrac{1}{3.4}\)+\(\dfrac{1}{4.5}\)+...+\(\dfrac{1}{x.\left(x+1\right)}\)=\(\dfrac{9}{20}\)
bài 2:tính
\(\dfrac{1}{4.5}\)+\(\dfrac{2}{5.7}\)+\(\dfrac{3}{7.10}\)+\(\dfrac{4}{10.14}\)+\(\dfrac{5}{14.19}\)+\(\dfrac{6}{19.25}\)
bài 3: tính
\(\left(1+\dfrac{1}{10}\right)\)\(\left(1+\dfrac{1}{11}\right)\)\(\left(1+\dfrac{1}{12}\right)\)...\(\left(1+\dfrac{1}{100}\right)\)
Bài 2:
\(\dfrac{1}{4\cdot5}+\dfrac{2}{5\cdot7}+\dfrac{3}{7\cdot10}+\dfrac{4}{10\cdot14}+\dfrac{5}{14\cdot19}+\dfrac{6}{19\cdot25}\)
\(=\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{10}+\dfrac{1}{10}-\dfrac{1}{14}+\dfrac{1}{14}-\dfrac{1}{19}+\dfrac{1}{19}-\dfrac{1}{25}\)
\(=\dfrac{1}{4}-\dfrac{1}{25}\)
\(=\dfrac{25}{100}-\dfrac{4}{100}\)
\(=\dfrac{21}{100}\)
Bài 3:
\(\left(1+\dfrac{1}{10}\right)\left(1+\dfrac{1}{11}\right)\left(1+\dfrac{1}{12}\right)...\left(1+\dfrac{1}{100}\right)\)
\(=\dfrac{10+1}{10}\cdot\dfrac{11+1}{11}\cdot\dfrac{12+1}{12}\cdot...\cdot\dfrac{100+1}{100}\)
\(=\dfrac{11}{10}\cdot\dfrac{12}{11}\cdot\dfrac{13}{12}\cdot...\cdot\dfrac{101}{100}\)
\(=\dfrac{11\cdot12\cdot13\cdot...\cdot101}{10\cdot11\cdot12\cdot...\cdot100}\)
\(=\dfrac{101}{10}\)
Bài 1:
\(\dfrac{1}{2\cdot3}+\dfrac{1}{3\cdot4}+...+\dfrac{1}{x\left(x+1\right)}=\dfrac{9}{20}\)
=>\(\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{x}-\dfrac{1}{x+1}=\dfrac{9}{20}\)
=>\(\dfrac{1}{2}-\dfrac{1}{x+1}=\dfrac{9}{20}\)
=>\(\dfrac{1}{x+1}=\dfrac{1}{2}-\dfrac{9}{20}=\dfrac{1}{20}\)
=>x+1=20
=>x=19(nhận)
