18:

a: \(S=3\left(\dfrac{2}{2\cdot4}+\dfrac{2}{4\cdot6}+...+\dfrac{2}{98\cdot100}\right)\)

=3*(1/2-1/4+1/4-1/6+...+1/98-1/100)

=3*49/100=147/100

b: Để A là số nguyên thì n-1 thuộc Ư(2)

=>n-1 thuộc {1;-1;2;-2}

=>n thuộc {2;0;3;-1}

1/2+1/6+1/12+1/20+...+1/380

=1/1.2+ 1/2.3+ 1/3.4+ 1/4.5+...+ 1/19.20

= 1/1-1/2+ 1/2-1/3+ 1/3-1/4+ 1/4-1/5+...+1/19-1/20

=1-1/29

=29/29-1/29

= 28/29

28/29

\(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{380}\)

\(=\frac{1}{1\times2}+\frac{1}{2\times3}+\frac{1}{3\times4}+\frac{1}{4\times5}+\frac{1}{19\times20}\)

\(=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{19}-\frac{1}{20}\)

\(=1-\frac{1}{29}\)

\(=\frac{28}{29}\)

\(=\dfrac{1}{2}\left(\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{10}\right)\)

\(=\dfrac{1}{2}\left(\dfrac{1}{2}-\dfrac{1}{10}\right)=\dfrac{1}{2}\cdot\dfrac{4}{10}=\dfrac{2}{10}=\dfrac{1}{5}\)

AI GIÚP MÌNH VỚI MÌNH ĐANG CẦN GẤP

1/3+1/6+1/12+1/24=8/24+4/24+2/24+1/24=15/24=5/8

tk cho mk nha!

\(\frac{1}{3}+\frac{1}{6}+\frac{1}{12}+\frac{1}{24}=\frac{8}{24}+\frac{4}{24}+\frac{2}{24}+\frac{1}{24}=\frac{15}{24}=\frac{5}{8}\)

\(\frac{5}{8}\)

~Hok tốt~

\(F=\frac{4}{2.4}+\frac{4}{4.6}+\frac{4}{6.8}+...+\frac{4}{2008.2010}\)

\(F=2.\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+...+\frac{1}{2008}-\frac{1}{2010}\right)\)

\(F=2.\left(\frac{1}{2}-\frac{1}{2010}\right)\)

\(F=2.\frac{502}{1005}\)

\(F=\frac{1004}{1005}\)

nhinf vào là biết luật ngay bài đó bằng = \(\frac{1004}{1005}\)

kết bạn với mình nha

\(F=\frac{4}{2.4}+\frac{4}{4.6}+\frac{4}{6.8}+...+\frac{4}{2008.2010}\)

\(\Rightarrow F=2\left(\frac{2}{2.4}+\frac{2}{4.6}+\frac{2}{6.8}+...+\frac{2}{2008.2010}\right)\)

\(\Rightarrow F=2\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+..+\frac{1}{2008}-\frac{1}{2010}\right)\)

\(\Rightarrow F=2\left(\frac{1}{2}-\frac{1}{2010}\right)\)

\(\Rightarrow F=2.\frac{502}{1005}\)

\(\Rightarrow F=\frac{1004}{1005}\)

Đặt A=1+1/3+1/6+1/10+ ... + 1/45

1/2.A=1/2+1/6+1/12+1/20+ ... + 1/90

1/2.A= 1/1.2+1/2.3+1/3.4+1/4.5+ ... + 1/9.10

1/2A= 1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+ ... +1/9-1/10

1/2.A= 1-1/10

1/2.A=9/10

A=(9/10).2

A=9/5

Sai thì thôi đấy 

bài này lớp 4 mà mình không làm được nhỉ . mình học dốt dốt quá .

a, 6/5

b,1