A=9.12+12.15+15.18-18.21

A=9.12+(12.15+15.18)-18.21

A=9.12+15.(12+18)-18.21

A=9.12+15.40-18.21

Vì 9.12 +15.40-18.21 chia hết cho2,3,,5,6,10,15

suy r a CHIA HÊT CHO 2,3,5,6,10,15

B tuong tự

k nhá Huyền hâm. tao nhắc cho mày rồi đấy nhá.

\(=\dfrac{1}{3}\left(\dfrac{1}{3}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{9}+...+\dfrac{1}{15}-\dfrac{1}{18}\right)\)

\(=\dfrac{1}{3}\left(\dfrac{1}{3}-\dfrac{1}{18}\right)=\dfrac{1}{3}\cdot\dfrac{5}{18}=\dfrac{5}{54}\)

\(\dfrac{5}{54}\)

Vì

\(\frac{1}{2}< \frac{2}{3};\frac{3}{4}< \frac{4}{5};\frac{5}{6}< \frac{6}{7};...;\frac{99}{100}< \frac{100}{101}\)

\(\Rightarrow\frac{1}{2}.\frac{3}{4}.\frac{5}{6}...\frac{99}{100}< \frac{2}{3}.\frac{4}{5}.\frac{6}{7}...\frac{100}{101}\)

\(\Rightarrow a< b\)

nhân 3 vào mỗi hạng tử ta được:

3*(1.2+2.3+3.4+...+99.100)

= 1.2.(3-0)+ 2.3.(4-1)+ 3.4.(5-2)+... + 99.100.(101-98)

=1.2.3 + 2.3.4 -1.2.3 + 3.4.5 -2.3.4 +... + 99.100.101 - 98.99.100

= 99.100.101

Vậy tổng ban đầu 99.100.101/3= 33.100.101

Vậy tổng trên chia hết cho 2;3;4;5;10

a/

\(1995^n.1997^n=\left(1995.1997\right)^n\)

\(1996^{2n}=\left(1996^2\right)^n\)

\(1995.1997=\left(1996-1\right).\left(1996+1\right)=1996^2-1\)

\(\Rightarrow1995.1997< 1996^2\Rightarrow1995^n.1997^n< 1996^{2n}\)

b/

\(A=\frac{1}{2.9}+\frac{1}{6.9}+\frac{1}{9.12}+\frac{1}{9.20}+\frac{1}{9.30}+\frac{1}{9.42}+\frac{1}{9.56}\)

\(A=\frac{1}{9}\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}\right)\)

\(A=\frac{1}{9}\left(\frac{2-1}{1.2}+\frac{3-2}{2.3}+\frac{4-3}{3.4}+...+\frac{8-7}{7.8}\right)\)

\(A=\frac{1}{9}\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{7}-\frac{1}{8}\right)\)

\(A=\frac{1}{9}\left(1-\frac{1}{9}\right)=\frac{1}{9}.\frac{8}{9}=\frac{8}{81}\)