có đầu óc thì phải suy nghĩ bạn ạ!!!

số đầu + số cuối  x khoảng cách :2 

mình cũng ko nhớ rõ

'''''''''' mình nha

A=1/2x3 + 1/3x4 + 1/4x5 + ... + 1/9x10

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

A= 1/2 - 1/10

Vậy A=2/5

Chúc bạn học tốt~~

\(\frac16+\frac{1}{12}+\frac{1}{20}+\cdots+\frac{1}{72}+\frac{1}{90}\)

\(=\frac{1}{2\times3}+\frac{1}{3\times4}+\frac{1}{4\times5}+\ldots+\frac{1}{8\times9}+\frac{1}{9\times10}\)

\(=\frac12-\frac13+\frac13-\frac14+\cdots+\frac18-\frac19+\frac19-\frac{1}{10}\)

\(=\frac12-\frac{1}{10}=\frac{4}{10}=\frac25\)

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

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

=   \(1\)\(-\)\(\frac{1}{8}\)

=    \(\frac{7}{8}\)

thiếu bước :v

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

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

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

\(\frac{1}{2}+\frac{1}{6}+...+\frac{1}{90}=\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+...+\frac{1}{9\cdot10}\)

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

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

\(=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}+\frac{1}{8.9}+\frac{1}{9.10}\)

\(=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{4}-\frac{1}{5}+\frac{1}{6}-\frac{1}{7}+\frac{1}{8}-\frac{1}{9}+\frac{1}{9}-\frac{1}{10}\)

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

\(y=\frac{1+5+11+19+29+41+55+71+89}{2+6+12+20+30+42+56+72+90}\)

\(y=\frac{1x2-1+2x3-1+3x4-1+4x5-1+5x6-1+6x7-1+7x8-1+8x9-1+9x10-1}{1x2+2x3+3x4+4x5+5x6+6x7+7x8+8x9+9x10}\)

\(y=\frac{\left(1x2+2x3+...+9x10\right)-\left(1+1+1+1+1+1+1+1+1\right)}{1x2+2x3+...+9x10}\)

\(y=\frac{1x2+2x3+...+9x10}{1x2+2x3+...+9x10}-\frac{9}{1x2+2x3+...+9x10}\)

\(y=1-\frac{9}{1x2+2x3+...+9x10}\)

\(\frac{1}{2}+\frac{5}{6}+\frac{11}{12}+\frac{19}{20}+\frac{29}{30}+\frac{41}{42}+\frac{55}{56}+\frac{71}{72}+\frac{89}{90}\) \(\frac{89}{90}\)

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

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

\(=9-\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}+\frac{1}{8.9}+\frac{1}{9.10}\right)\) 

\(=9-\frac{11}{10}\)

\(=\frac{79}{10}\)

~Học tốt nha~

Đặt : \(A=\frac{1}{2}+\frac{5}{6}+\frac{11}{12}+\frac{19}{20}+\frac{29}{30}+\frac{41}{42}+\frac{55}{56}+\frac{71}{72}+\frac{89}{90}\)

\(\Leftrightarrow A=\left(1-\frac{1}{2}\right)+\left(1-\frac{1}{6}\right)+......+\left(1-\frac{1}{90}\right)\)

\(\Leftrightarrow A=\left(1+1+....+1\right)-\left(\frac{1}{2}+\frac{1}{6}+....+\frac{1}{90}\right)\)

\(\Leftrightarrow A=9-\left(\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{9.10}\right)\)

\(\Leftrightarrow A=9-\left(1-\frac{1}{10}\right)\)

\(\Leftrightarrow A=9-\frac{9}{10}=\frac{81}{90}\)

\(A=\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{30}+...+\frac{1}{72}+\frac{1}{81}\)

\(A=\frac{1}{1\times2}+\frac{1}{2\times3}+\frac{1}{3\times4}+...+\frac{1}{8\times9}+\frac{1}{81}\)

\(A=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{8}-\frac{1}{9}+\frac{1}{81}\)

\(A=1-\frac{1}{9}+\frac{1}{81}=\frac{73}{81}\)

\(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+\frac{1}{81}\)

\(=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{8.9}+\frac{1}{81}\)

\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{8}-\frac{1}{9}+\frac{1}{81}\)

\(=1-\frac{1}{9}+\frac{1}{81}\)

\(=\frac{8}{9}+\frac{1}{81}\)

\(=\frac{73}{81}\)

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

bn vào câu hỏi tương tự sẽ có chi tiết . Nếu k thì bn hãy để ý mỗi tử đều bé hơn mẫu 1 đơn vị sau đó bn tách ra bằng cách lấy 1 trừ . VD: 5/6 bằng 1  -  1/6 . Đến đó đếm đc 9 chữ số 1 ta lấy 9 làm sbt trừ đi tổng của các ps ta tách đc . Khi đó thì bài toán quá đơn giản rồi . Chúc bn học tốt

(1-1/2)+(1-1/6)+...+(1-1/90)

9+(1/2+1/6+...+1/90)

9+(1/1.2+1/2.3+...+1/9.10)

9+1-9/10=9/1/10=91/10