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) \(\frac{18}{109}và\frac{5}{30}\)

E= ( 1+ \(\frac{1}{2}\)) . (1+\(\frac{1}{3}\)) . (1+\(\frac{1}{4}\)) ... (1+\(\frac{1}{99}\))

H= 1\(\frac{1}{2}.1\frac{1}{3}.1\frac{1}{4}...1\frac{1}{2015}\)

D= 1+\(\frac{1}{3}\)+\(\frac{1}{3^2}+\frac{1}{3^3}+...+\frac{1}{3^n}\)
G= (1-\(\frac{1}{2}\)) . ( 1-\(\frac{1}{3}\)) . (1-\(\frac{1}{4}\))....(1-\(\frac{1}{2015}\)