Chứng minh rằng:

\(\frac{1}{2.2}+\frac{1}{4.4}+\frac{1}{6.6}+.....+\frac{1}{200.200}< \frac{1}{4}\) 

\(Chứng\)\(minh\)rằng

\(\frac{1}{2.2}+\frac{1}{4.4}+\frac{1}{6.6}+\frac{1}{8.8}+....+\frac{1}{200.200}< \frac{1}{2}\)

Cho A = \(1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{9}-\frac{1}{10}\)

B = \(\left(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{10}\right)-2\left(\frac{1}{2}+\frac{1}{4}+...+\frac{1}{10}\right)\)

a) So sánh A và B

b) Chứng minh A = \(\frac{1}{6}+\frac{1}{7}+\frac{1}{8}+\frac{1}{9}+\frac{1}{10}\)

bài 1: tính A:=\(\frac{1}{2}-\frac{2}{3}+\frac{3}{4}-\frac{4}{5}+\frac{5}{6}-\frac{6}{7}-\frac{5}{6}+\frac{4}{5}-\frac{3}{4}+\frac{2}{3}-\frac{2}{3}-\frac{1}{2}\)

Bài 2: Cho B=\(1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+\frac{1}{5}-\frac{1}{6}+.....+\frac{1}{49}-\frac{1}{50}\)

Chứng minh rằng: \(\frac{7}{12}< A< \frac{5}{6}\)

Cho a, b,c,d dương.

Chứng minh rằng \(\frac{2a}{a^6+b^4}+\frac{2b}{b^6+c^4}+\frac{2c}{c^6+a^4}\le\frac{1}{a^4}+\frac{1}{b^4}+\frac{1}{c^4}\)

Chứng minh rằng: Nếu \(\frac{a}{b}=\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}+\frac{1}{7}+\frac{1}{8}+\frac{1}{9}+\frac{1}{10}​\)

Thì a chia hết cho 13

a) Chứng minh: \(\frac{11}{15}< \frac{1}{21}+\frac{1}{22}+\frac{1}{23}+...+\frac{1}{60}< \frac{3}{2}\)

b) Chứng minh: \(3< 1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{63}< 6\)

Tính A = \(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}+.........+\frac{1}{31}\)

Chứng minh A < 4

Cho \(A=\frac{1}{5^2}+\frac{1}{6^2}+\frac{1}{7^2}+...+\frac{1}{100^2}\)

Chứng minh rằng 1/6 < A < 1/4