với mọi $n\geq 1,n\epsilon N$.c/m:
a)$\frac{1}{n+1}+\frac{1}{n+2}+...+\frac{1}{2n}< \frac{7}{10}$
b)$1+\frac{1}{2^{2}}+\frac{1}{3^{2}}+...+\frac{1}{n^{2}}< \frac{79}{48}$
c)$\frac{1}{n+1}+\frac{1}{n+2}+...+\frac{1}{n+n}\geq \frac{2}{3}$ với $n\geq 3$
d)$1+\frac{1}{\gamma 2}+\frac{1}{\gamma 3}+...+\frac{1}{\gamma n}< 2\gamma n$ với $n\geq 1$
e)$1^{3}+3^{3}+5^{3}+...+(2n+1)^{3}> 2(n+1)^{3}(2n+1)$
g)$1^{4}+2^{4}+3^{4}+...+n^{4}> \frac{n^{2}(n+1)^{2}(2n+1)}{10}$
h)$\gamma 2+\gamma 3^{2}+\gamma 4^{3}+...+\gamma (n+1)^{n}< (n+1)$
k)$1+\frac{1}{2^{3}}+...+\frac{1}{n^{3}}< \frac{5}{4}$