Sửa đề: \(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+\frac{1}{15}+..+\frac{1}{120}\)

Đặt A=\(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+\frac{1}{15}+...+\frac{1}{120}\)

\(\frac{1}{2}A=\frac{1}{2}\left(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{1}{120}\right)\)

\(\frac{1}{2}A=\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{240}\)

\(\frac{1}{2}A=\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+...+\frac{1}{15\cdot16}\)

\(\frac{1}{2}A=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{15}-\frac{1}{16}\)

\(\frac{1}{2}A=\frac{1}{2}-\frac{1}{16}\)

\(A=\frac{7}{16}:\frac{1}{2}\)

\(A=\frac{7}{8}\)

ủa cái này là tính nhanh nè

\(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+\frac{1}{15}+...+\frac{1}{45}\)

\(=\frac{2}{6}+\frac{2}{12}+\frac{2}{20}+\frac{2}{30}+...+\frac{2}{90}\)

\(=\frac{2}{2.3}+\frac{2}{3.4}+\frac{2}{4.5}+\frac{2}{5.6}+...+\frac{2}{9.10}\)

\(=2.\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+..+\frac{1}{9}-\frac{1}{10}\right)\)

\(=2.\left(\frac{1}{2}-\frac{1}{10}\right)\)

\(=2.\frac{2}{5}=\frac{4}{5}\)

\(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+\frac{1}{15}+...+\frac{1}{45}\)

\(=\frac{2}{6}+\frac{2}{12}+\frac{2}{20}+\frac{2}{30}+...+\frac{2}{90}\)

\(=\frac{2}{2.3}+\frac{2}{3.4}+\frac{2}{4.5}+\frac{2}{5.6}+...+\frac{2}{9.10}\)

\(=2.\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{9}-\frac{1}{10}\right)\)

\(=2.\left(\frac{1}{2}-\frac{1}{10}\right)\)

\(=\frac{4}{5}\)

\(\frac{9}{11}\)nha kb đi

lấy (1/3 + 1/15 +1/10 + 1/21 ) + (1/36 + 1/28 + 1/6) + (1/45 + 1/55)

      =  (4/50 + 3/70) + 2/100

      = 7/120 + 2/100

      = 9/220

Cách giải

X = 8/9 / ( 1+1/3+1/6+1/10+1/15+1/21)

1+1/3=4/3

4/3+1/6=3/2

3/2+1/10=8/5

8/5+1/15=5/3

5/3+1/21=12/7

4/3+3/2=17/6

8/5+5/3=49/15

(17/6+49/15)+17/6=183/30+17/6=286/30

8/9:286/30=2288/270=1140/135=228/27=76/9

X = 76/9

\(A=\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+...+\frac{1}{2004\cdot2005}+\frac{1}{2005\cdot2006}\)

\(A=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{2004}-\frac{1}{2005}+\frac{1}{2005}-\frac{1}{2006}\)

\(A=1-\frac{1}{2006}=\frac{2005}{2006}\)

\(A=\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{2005.2006}\)

\(\Rightarrow A=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{2005}-\frac{1}{2006}\)

\(\Rightarrow A=1-\frac{1}{2006}\)

\(\Rightarrow A=\frac{2005}{2006}\)

Bài 2: Tính bằng cách thuận tiện nhất :

1/2+2/4+3/6+4/8+5/10+6/12=3

1/3+1/4+1/5+8/10+20/15+20/30=43/12

Sai đầu bài bạn ơi ! Bạn xem lại giúp mình sau đó thay đổi đầu bài mình giải cho

C=\(\frac{1}{3}+\frac{1}{10}+\frac{1}{15}+\frac{1}{20}+\frac{1}{25}+\frac{1}{30}+\frac{1}{35}+\frac{1}{40}\)

=\(\frac{1}{3}+\frac{1}{15}+\frac{1}{10}+\frac{1}{20}+\frac{1}{30}+\frac{1}{40}+\frac{1}{25}+\frac{1}{35}\)

=\(\frac{5}{15}+\frac{1}{15}+\frac{4}{40}+\frac{2}{40}+\frac{1}{40}+\frac{1}{30}+\frac{1}{25}+\frac{1}{35}\)

=\(\frac{6}{15}+\frac{7}{40}+\frac{107}{1050}\)

a) \(\frac{1}{3}+\frac{1}{4}-\frac{1}{5}\)

\(=\frac{23}{60}\)

b) \(\frac{5}{2}+\frac{1}{3}-\frac{1}{4}\)

\(=\frac{31}{12}\)

c) \(\frac{10}{3}-\left(\frac{1}{4}+\frac{1}{12}\right)\)

\(=\frac{9}{3}=3\)

d) \(\frac{1}{3}+\frac{6}{5}-\frac{1}{15}\)

\(=\frac{22}{15}\)

trả lòi:

A)= 23/60

B)= 31/12

C)= 3* vì 3/9 cùng chia hết cho 3*

D)= 22/15

Hc tốt!