`1.

a/Chứng minh rằng: \(\frac{1}{41}\)+\(\frac{1}{42}\)+\(\frac{1}{43}\)+...+\(\frac{1}{80}\)>\(\frac{7}{12}\)

b/Chứng minh rằng:: \(\frac{1}{41}\)+\(\frac{1}{42}\)+\(\frac{1}{43}\)+...+\(\frac{1}{60}\)>\(\frac{1}{3}\)

c//Chứng minh rằng:: \(\frac{1}{61}\)+\(\frac{1}{62}\)+\(\frac{1}{62}\)+...+\(\frac{1}{80}\)>\(\frac{1}{4}\)

2.Cho phân số\(\frac{a}{b}\)=\(\frac{1}{6}\)+\(\frac{1}{7}\)+\(\frac{1}{8}\)+\(\frac{1}{9}\)+\(\frac{1}{10}\)+\(\frac{1}{11}\)với a,b thuộc N. Chứng minh rằng a chia hết cho 17

\(\frac{1}{6}\)

a) \(Cho\)\(S=\frac{1}{31}+\frac{1}{32}+\frac{1}{33}+.....+\frac{1}{60}\)

\(Chứng\) \(minh\) \(\frac{3}{5}< S< \frac{4}{5}\)

b) \(Chứng\)\(minh\)\(\frac{1}{41}+\frac{1}{42}+\frac{1}{43}+.....+\frac{1}{100}>\frac{7}{10}\)

c) \(Chứng\)\(minh\)\(\frac{3}{10}+\frac{3}{11}+\frac{3}{12}+\frac{3}{13}+\frac{3}{14}\) không là số tự nhiên

d) \(Chứng\)\(minh\)\(\frac{1}{5}< D< \frac{1}{10}\) \(với\)\(D=\frac{1}{2}.\frac{3}{4}.\frac{5}{6}.....\frac{99}{100}\)

tính nhanh

1) A=\(\frac{-15}{19}\).\(\frac{23}{37}\)+\(\frac{14}{37}\).\(\frac{15}{19}\)

2)B=\(\frac{9}{11}\).\(\frac{-6}{13}\)-\(\frac{16}{13}\).\(\frac{9}{11}\)+\(\frac{9}{11}\).\(\frac{25}{13}\)

3)C=\(\frac{16}{111}\).\(\frac{-7}{12}\)-\(\frac{-14}{12}\).\(\frac{8}{111}\)

4)D=\(\frac{1}{10.11}\)+\(\frac{1}{11.12}\)+...+\(\frac{1}{101.102}\)+\(\frac{1}{102.103}\)

5)E=\(\frac{3}{4}\)+\(\frac{3}{28}\)+\(\frac{3}{70}\)+\(\frac{3}{130}\)

Cho M=\(\frac{1}{10}\)+\(\frac{1}{11}\)+\(\frac{1}{12}\)+\(\frac{1}{13}\)+\(\frac{1}{14}\)+\(\frac{1}{15}\)+\(\frac{1}{16}\)+\(\frac{1}{17}\)+\(\frac{1}{18}\)+\(\frac{1}{19}\)+\(\frac{1}{20}\)

Chứng​ minh: \(\frac{11}{15}\)<M<\(\frac{5}{6}\)

Ai nhanh mình tick

bài 1: tính hợp lí

 A = \(\frac{1}{3}\). \(\frac{-6}{13}\) . \(\frac{-9}{10}\) . \(\frac{-13}{36}\)

B = \(\frac{-5}{12}\) .  \(\frac{4}{19}\)+ \(\frac{-7}{12}\) . \(\frac{4}{19}\) - \(\frac{40}{57}\)

C = \(\frac{3}{7}\) . \(\frac{9}{26}\) - \(\frac{1}{14}\) . \(\frac{1}{13}\) - \(\frac{1}{7}\)

D = \(\frac{1}{3}\) . \(\frac{4}{5}\) + \(\frac{1}{3}\) . \(\frac{6}{5}\) + \(\frac{2}{3}\)

Ai làm nhanh mình tik, giải rõ giúp mình, mình đang cần gấp, cảm ơn

tính

D = \(\frac{5}{7}\). \(\frac{12}{11}\)\(+\)\(\frac{5}{7}\). \(\frac{12}{11}\)\(-\)\(\frac{5}{7}\). \(\frac{17}{11}\)

E = /\(\frac{1}{4}\)\(-\)\(\frac{2}{3}\)/\(-\)3 (\(\frac{2}{3}\)\(-\)\(\frac{1}{4}\)) \(+\)\(\frac{60}{13}\)\(-\)(\(\frac{3}{13}\))\(^2\)

a, (  2 +\(\frac{5}{6}\)) :\(1\frac{1}{5}\)+\(\frac{-7}{12}\)

b,(15 - \(6\frac{13}{18}\)) : \(11\frac{1}{7}\)-\(2\frac{1}{8}\):\(1\frac{11}{40}\)

c,(-3,2).\(\frac{-15}{64}\)+ (0,8 -\(2\frac{4}{15}\)) :\(3\frac{2}{3}\)