A=1/13.14+1/14.15+1/15.16+1/16.17=1/17.18+1/18.19

A=1/13-1/14+1/14-1/15+1/15-1/16+1/16-1/17+1/18-1/19

A=1/13-1/19

A=6/247

a)     5/30+15/90+25/150+35/210+45/270

       =1/6+1/6+1/6+1/6+1/6

       =1/6 x 5

       =5/6

b)     1/2+1/6+1/12+1/20+....+1/56

        =1/1x2+1/2x3+1/3x4+1/4x5+.....1/7x8

        =1/1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+.......-1/7+1/7-1/8

        =1/1-1/8

         =7/8

c)     mình chịu

thank you bn nhìu nha

chịu,khó quá,nhất là câu c ý

A = \(\frac{-79}{90}\)

B = \(\frac{8}{9}\)

cách giải sao chỉ mình với

\(\frac{1}{2}\)+   \(\frac{1}{6}\)+   \(\frac{1}{12}\)+  \(\frac{1}{20}\)+   \(\frac{1}{30}\)+   \(\frac{1}{42}\)+    \(\frac{1}{56}\)

=   \(\frac{1}{1.2}\)+   \(\frac{1}{2.3}\)+    \(\frac{1}{3.4}\)+   \(\frac{1}{4.5}\)+   ......   +   \(\frac{1}{7.8}\)

=   \(1\)\(-\)\(\frac{1}{8}\)

=    \(\frac{7}{8}\)

thiếu bước :v

\(=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{7}-\frac{1}{8}\)

\(=1-\frac{1}{8}\)

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

\(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}\)

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

\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}\)

\(=1-\frac{1}{8}\)

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

từ đầu bài ta có

1 phần 6 cộng một phần12 cộng..... cộng một phần 42

=1phần 2.3 +1 phần 3.4 +....+1 phần6.7

=1 phần2 -(1 phần 3 +1 phần 3)...........-(1 phần 6 +1 phần 6)-1 phần 7

1 phần 2 -1 phần 7

=5 phần 14 

mongcasc bạn giúp mk mai mk ktra chương, tất nhiên mk sẽ k cho ai nhanh mà đúng

Ta có:

\(\frac{1}{n\left(n+1\right)}=\frac{n+1-n}{n\left(n+1\right)}=\frac{n+1}{n\left(n+1\right)}-\frac{n}{n\left(n+1\right)}=\frac{1}{n}-\frac{1}{n+1}\)

\(\Rightarrow A=\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}\)

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

\(A=\frac{1}{2}-\frac{1}{7}\)

\(A=\frac{5}{14}\)

\(E=\frac{2}{20}+\frac{2}{30}+...+\frac{2}{240}\)

\(\Rightarrow E=\frac{2}{4.5}+\frac{2}{5.6}+...+\frac{2}{15.16}\)

\(E=2.\left(\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+...+\frac{1}{15}-\frac{1}{16}\right)\)

\(E=2.\frac{3}{16}=\frac{3}{8}\)

\(E=\frac{2}{20}+\frac{2}{30}+\frac{2}{42}+...+\frac{2}{240}\)

\(E=\frac{2}{4.5}+\frac{2}{5.6}+\frac{2}{6.7}+...+\frac{2}{15.16}\)

\(E=2.\left(\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+...+\frac{1}{15}-\frac{1}{16}\right)\)

\(E=2.\left(\frac{1}{4}-\frac{1}{16}\right)\)

\(E=2.\frac{3}{16}\)

\(E=\frac{3}{8}\)

\(D=\frac{1}{6}+\frac{1}{66}+\frac{1}{176}+...+\frac{1}{336}\)

\(D=\frac{1}{1.6}+\frac{1}{6.11}+\frac{1}{11.16}+...+\frac{1}{16.21}\)

\(D=\frac{1}{5}.\left(1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+\frac{1}{11}-\frac{1}{16}+...+\frac{1}{16}-\frac{1}{21}\right)\)

\(D=\frac{1}{5}.\left(1-\frac{1}{21}\right)\)

\(D=\frac{1}{5}.\frac{20}{21}\)

\(D=\frac{4}{21}\)

1/2+1/6+1/12+...+1/110

=1/1.2+1/2.3+1/3.4+...+1/10.11

=1-1/2+1/2-1/3+1/3-1/4+...+1/10-1/11

=1-1/11=10/11

1/2

Ta có : 

\(1-\frac{1}{2}-\frac{1}{6}-\frac{1}{12}-\frac{1}{20}-\frac{1}{30}-...-\frac{1}{110}\)

\(=\)\(1-\left(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+...+\frac{1}{110}\right)\)

\(=\)\(1-\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{10.11}\right)\)

\(=\)\(1-\left(\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{10}-\frac{1}{11}\right)\)

\(=\)\(1-\left(1-\frac{1}{11}\right)\)

\(=\)\(1-1+\frac{1}{11}\)

\(=\)\(\frac{1}{11}\)

Chúc bạn học tốt ~ 

\(1-\frac{1}{2}-\frac{1}{6}-\frac{1}{12}-...-\frac{1}{110}\)

\(=1-\left(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+...+\frac{1}{110}\right)\)

\(=1-\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{10.11}\right)\)

\(=1-\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{10}-\frac{1}{11}\right)\)

\(=1-\left(1-\frac{1}{11}\right)\)

\(=1-\frac{10}{11}\)

\(=\frac{1}{11}\)

Chúc bạn học tốt !!! 

Đặt \(A=1-\frac{1}{2}-\frac{1}{6}-...-\frac{1}{110}\)

\(\Rightarrow-A=-1+\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{10.11}\)

\(\Rightarrow-A=-1+1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{10}-\frac{1}{11}\)

\(\Rightarrow-A=-\frac{1}{11}\Rightarrow A=\frac{1}{11}\)

\(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+\frac{1}{90}\)

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

\(=1-\frac{1}{10}=\frac{9}{10}\)

Bạn biết bài này rồi phải không =.="

Bài này hỏi nhiều rồi !

Kết quả là : 9/10
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