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

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

Bài 5 : Chững minh rẳng :
a) S= \(\frac{3}{10}+\frac{3}{11}+\frac{3}{12}+\frac{3}{13}+\frac{3}{14}\) CMR :1< S <2
b) \(\frac{1}{4^2}+\frac{1}{6^2}+\frac{1}{8^2}+\frac{1}{10^2}+...+\frac{1}{\left(2n\right)^2}< \frac{1}{4}\)
c) \(\frac{3}{4}+\frac{8}{9}+\frac{15}{16}+...+\frac{2499}{2500}>48\)
d) \(\frac{1}{5}+\frac{1}{13}+\frac{1}{14}+\frac{1}{15}+\frac{1}{61}+\frac{1}{62}+\frac{1}{63}< \frac{1}{2}\)
Bài :So sánh phân số sau:
a)\(\frac{1985.1987-1}{1980+1985.1986}và1\)
b) A= \(\frac{13^{15}+1}{13^{16}+1}\)và B = \(\frac{13^{16}+1}{13^{17}+1}\)
c)\(\frac{18}{53}và\frac{26}{79}\)
d)\(\frac{5}{8}và\frac{14}{17}\)
e)\(\frac{1}{5^{199}}và\frac{1}{3^{300}}\)
g)\(\frac{1}{3^{17}}và\frac{1}{5^{10}}\)
h) \(\frac{18}{109}và\frac{5}{30}\)

Bài 1:Tìm x biết Bài 2:So sánh

a, \(x+\frac{1}{2}=\frac{3}{8}.\frac{4}{5}\) a, \(A=\frac{10^{10}-1}{10^{11}-1}vaB=\frac{10^9-1}{10^{10}-1}\)

b, \(\frac{5}{16}:x-\frac{1}{4}=\frac{5}{8}\) b, B =\(\frac{10^{10}}{10^{10}+1}vaB=\frac{10^{10}+1}{10^{10}+2}\)

c, \(\frac{-1}{4}.x+\frac{3}{7}.x=2\)

d, \(\frac{22}{9}-\left(x+\frac{1}{2}\right)^2=\frac{7}{3}\)

e, \(\left|\frac{1}{4}-x\right|+5\frac{1}{8}=6\frac{1}{8}\)

bài 1 tính nhanh

a) 3\(\frac{1}{417}\). \(\frac{1}{762}\)-\(\frac{1}{139}\).\(4\frac{761}{762}\)-\(\frac{4}{417.762}\)+\(\frac{5}{139}\)

b) \(5\frac{4}{23}\). \(27\frac{3}{27}\)+ \(4\frac{8}{27}\).\(-5\frac{4}{23}\)

c) \(3\frac{10}{99}\). \(6\frac{1}{4}\)+ \(3\frac{2}{5}\).\(3\frac{3}{4}\)

bài 2 tính tổng

S= 1+2+5+14+...+ \(\frac{3^n+1}{2}\)

Tính : 

a) A=2\(\frac{3}{7}\):(-12\(\frac{1}{2}\)+  15\(\frac{1}{7}\)) . (-3\(\frac{3}{10}\)) - (-\(\frac{34}{37}\)) . (2\(\frac{1}{10}\)-4\(\frac{2}{5}\))

b)B=3\(\frac{1}{10}\):(\(\frac{1}{2}\)-\(\frac{2}{5}\)) - 2\(\frac{1}{28}\): (\(\frac{2}{7}\)- \(\frac{3}{4}\))

bài 2 tìm x

a,\(\frac{-2}{3}.x+\frac{1}{5}=\frac{3}{10}\)

b,\(\left|x\right|-\frac{3}{4}=\frac{5}{3}\)

c,\(\frac{2}{3}.x-\frac{1}{2}=\frac{1}{10}\)

d,\(\frac{3}{5}+\frac{4}{9}:x=\frac{2}{3}\)

e,\(\left|x+75\%\right|=2\frac{1}{5}\)

i,\(\left(x+\frac{1}{2}\right).\left(\frac{2}{3}-2.x\right)=0\)

k,\(\frac{4}{7}.x-\frac{2}{3}=\frac{1}{5}\)

l,\(\frac{2}{3}.x-\frac{3}{2}.x=\frac{5}{12}\)

m,\(\left|2.x-\frac{1}{3}\right|+\frac{5}{6}=1\)

n,\(\frac{1}{3}-\frac{7}{8}.x=\frac{1}{3}\)

11,\(\frac{x+2}{5}=\frac{7}{12}-1\frac{1}{4}\)

12,\(\left(2\frac{4}{5}.x-50\right):\frac{2}{3}=51\)

13,\(\frac{2}{5}+\frac{3}{5}.\left(3.x-3,7\right)=-\frac{53}{10}\)

14,\(\frac{7}{9}:\left(2+\frac{3}{4}.x\right)+\frac{5}{9}=\frac{23}{27}\)

a,\(\frac{-5}{6}\) - x = \(\frac{7}{12}\) + \(\frac{-1}{3}\)

b,\(\frac{x+3}{-15}\) = \(\frac{1}{3}\)

c, \(\frac{-15}{x-1}\)=\(\frac{-3}{5}\)

d,\(\frac{1}{2}\)x-\(\frac{2}{5}\)=\(\frac{1}{5}\)

e,-\(\frac{2}{3}\)x+\(\frac{1}{5}\)=\(\frac{1}{10}\)

f,\(\frac{4}{5}\)- \(\frac{1}{2}\)x = \(\frac{1}{10}\)

bài 1

a,\(\frac{x}{5}\)=\(\frac{2}{3}\)

b,\(\frac{x}{3}\)-\(\frac{1}{2}\)=\(\frac{1}{5}\)

c,\(\frac{x}{5}\)+\(\frac{1}{2}\)=\(\frac{6}{10}\)

d,\(\frac{x+3}{15}\)=\(\frac{1}{3}\)

e,\(\frac{x-12}{4}\)=\(\frac{1}{2}\)

h,\(\frac{4}{5}\)+x=\(\frac{2}{3}\)

i,\(\frac{3}{4}\)-x=\(\frac{1}{3}\)

k,\(\frac{-5}{6}\)-x=\(\frac{2}{3}\)

l,x-\(\frac{5}{9}\)=\(\frac{-2}{3}\)

m,\(\frac{1}{2}\)x+\(\frac{1}{2}\)=\(\frac{5}{2}\)

n,\(\frac{-2}{3}\)-\(\frac{1}{3}\)(2x-5)=\(\frac{3}{2}\)

p,(3x-1)(\(-\frac{1}{2}\)x+5)=0

q,\(3\frac{1}{3}\)+\(\frac{5}{6}\)x=\(3\frac{1}{2}\)

s,\(\frac{1}{2}\)-\(\frac{2}{3}\)x=\(\frac{7}{12}\)

t,\(\frac{3}{4}\)x+\(\frac{1}{5}\)=\(\frac{1}{6}\)

u,\(\frac{3}{8}\)-\(\frac{1}{6}\)x=\(\frac{1}{4}\)

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