A = \(\frac{-79}{90}\)

B = \(\frac{8}{9}\)

cách giải sao chỉ mình với

9/1-1/90-1/72-1/56-1/42-1/30-1/20-1/12-1/6-1/2=0/4

Giải :

ta có

  \(\frac{9}{10}-\left(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+...+\frac{1}{90}\right)\)

=\(\frac{9}{10}-\left(\frac{1}{1\times2}+\frac{1}{2\times3}+...+\frac{1}{9\times10}\right)\)

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

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

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

=\(\frac{9}{10}-1+\frac{1}{10}=0\)                  (Mong online math ks cho mình nhé)

\(A=\frac{1}{10}-\left(\frac{1}{20}+\frac{1}{30}+....+\frac{1}{90}\right)=\frac{1}{10}-\left(\frac{1}{4.5}+\frac{1}{5.6}+.....+\frac{1}{9.10}\right)\)

\(=\frac{1}{10}-\left(\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+...-\frac{1}{10}\right)=\frac{1}{10}-\left(\frac{1}{4}-\frac{1}{10}\right)=\frac{1}{5}-\frac{1}{4}=\frac{-1}{20}\)

\(A=\frac{1}{10}-\frac{1}{20}-\frac{1}{30}-\frac{1}{42}-\frac{1}{56}-\frac{1}{72}-\frac{1}{90}\)

\(A=\frac{1}{10}-\left(\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+...+\frac{1}{90}\right)\)

\(A=\frac{1}{10}-\left(\frac{1}{4.5}+\frac{1}{5.6}+...+\frac{1}{9.10}\right)\)

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

\(A=\frac{1}{10}-\left[\left(\frac{1}{4}-\frac{1}{10}\right)-\left(\frac{1}{5}-\frac{1}{5}\right)-...-\left(\frac{1}{9}-\frac{1}{9}\right)\right]\)

\(A=\frac{1}{10}-\frac{1}{4}+\frac{1}{10}\)

\(A=\frac{1}{5}-\frac{1}{4}\)

\(A=-\frac{1}{20}\)

\(A=\frac{9}{10}-\frac{1}{90}-\frac{1}{72}-\frac{1}{56}-...-\frac{1}{6}-\frac{1}{2}\)

\(A=\frac{9}{10}-\left(\frac{1}{2}+\frac{1}{6}+...+\frac{1}{56}+\frac{1}{72}+\frac{1}{90}\right)\)

\(A=\frac{9}{10}-\left(\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{7.8}+\frac{1}{8.9}+\frac{1}{9.10}\right)\)

\(A=\frac{9}{10}-\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}+\frac{1}{9}-\frac{1}{10}\right)\)

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

\(A=\frac{9}{10}-\frac{9}{10}=0\)

\(A=\frac{9}{10}-\frac{1}{90}-\frac{1}{72}-\frac{1}{56}-...-\frac{1}{6}-\frac{1}{2}\)

\(\Leftrightarrow A=\frac{9}{10}-\left(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+...+\frac{1}{90}\right)\)

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

\(\Leftrightarrow A=0\)

kết quả = 0

\(\frac{9}{10}-\frac{1}{90}-\frac{1}{72}-\frac{1}{56}-\frac{1}{42}-\frac{1}{30}-\frac{1}{20}-\frac{1}{12}-\frac{1}{6}-\frac{1}{2}\)

=\(\frac{9}{10}-\frac{1}{10.9}-\frac{1}{9.8}-\frac{1}{8.7}-\frac{1}{7.6}-\frac{1}{6.5}-\frac{1}{5.4}-\frac{1}{4.3}-\frac{1}{3.2}-\frac{1}{2.1}\)

=\(\frac{9}{10}-(\frac{1}{10.9}-\frac{1}{9.8}-\frac{1}{8.7}-\frac{1}{7.6}-\frac{1}{6.5}-\frac{1}{5.4}-\frac{1}{4.3}-\frac{1}{3.2}-\frac{1}{2.1})\)

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

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

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

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

= \(\frac{-2}{10}=-\frac{1}{5}\)

# Chúc bạn học tốt #

\(\frac{9}{10}-\frac{1}{90}-\frac{1}{72}-\frac{1}{56}-...-\frac{1}{6}-\frac{1}{2}\)

\(=\frac{9}{10}-\left(\frac{1}{9.10}+\frac{1}{8.9}+\frac{1}{7.8}+...+\frac{1}{2.3}+\frac{1}{1.2}\right)\)

\(=\frac{9}{10}-\left(\frac{1}{9}-\frac{1}{10}+\frac{1}{8}-\frac{1}{9}+\frac{1}{7}-\frac{1}{8}+...+\frac{1}{2}-\frac{1}{3}+\frac{1}{1}-\frac{1}{2}\right)\)

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

\(=0\)

Hi Hi!

Đầu tiên , ta cộng các phần nguyên lại với nhau trước :

 ( 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 ) + ( \(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{8}{72}+\frac{1}{90}+\frac{1}{10}\)

= 45 + \(\left(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{42}+\frac{1}{72}\right)+\left(\frac{1}{10}+\frac{1}{20}\right)+\left(\frac{1}{30}+\frac{1}{90}\right)+\frac{1}{56}\)

= 45 + 

tới đây tớ chịu , các cậu giúp với

Đầu tiên , cộng các phần nguyên lại với nhau , ta có :

( 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 ) + ( \(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+\frac{1}{90}+\frac{1}{10}\))

= 45 + \(\left(\frac{1}{6}+\frac{1}{30}\right)+\frac{1}{2}+\frac{1}{12}+\frac{1}{20}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+\frac{1}{90}+\frac{1}{10}\)

sau khi cộng trong ngoặc , ta được 6 / 30 , rút gọn tối giản còn 1 / 5 

= 45 + \(\left(\frac{1}{5}+\frac{1}{20}\right)+\frac{1}{2}+\frac{1}{12}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+\frac{1}{90}+\frac{1}{10}\)

sau khi cộng trong ngoặc và rút gọn tối giản , ta được 1 / 4 

= 45 + \(\left(\frac{1}{4}+\frac{1}{2}\right)+\frac{1}{12}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+\frac{1}{90}+\frac{1}{10}\)

sau khi cộng trong ngoặc rồi rút gọn  , ta được 3 / 4

= 45 + \(\left(\frac{3}{4}+\frac{1}{12}\right)+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+\frac{1}{90}+\frac{1}{10}\)

rút gọn lại ta được 5 / 6 

= 45 + \(\left(\frac{5}{6}+\frac{1}{42}\right)+\frac{1}{56}+\frac{1}{72}+\frac{1}{90}+\frac{1}{10}\)

rút gọn tối giản ra 6 / 7

= 45 + \(\left(\frac{6}{7}+\frac{1}{56}\right)+\frac{1}{72}+\frac{1}{90}+\frac{1}{10}\)

sau khi tính trong ngoặc rút gọn được 7 / 8

= 45 + \(\left(\frac{7}{8}+\frac{1}{72}\right)+\frac{1}{90}+\frac{1}{10}\)

tính trong ngoặc rồi rút gọn ra 8 / 9 

= 45 + \(\left(\frac{8}{9}+\frac{1}{90}\right)+\frac{1}{10}\)

cũng rút gọn tiếp ta được 9 / 10

= 45 + \(\left(\frac{9}{10}+\frac{1}{10}\right)\)

= 45 + 1

= 46

cái này thì bạn lên làm giảng viên đến nơi rồi

1/2+6+12+20+30+42+56+72+90

=1/90

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

\(=\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+\frac{1}{5\cdot6}+\frac{1}{6\cdot7}+\frac{1}{7\cdot8}+\frac{1}{8\cdot9}+\frac{1}{9\cdot10}\)

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

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

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

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

\(=\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+...+\frac{1}{9\cdot10}\)

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

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

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