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

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

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

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

= 1 - 1 = 0

Vậy kết quả của phép tính là 0

Ta có : 
9/10-1/90-1/72-1/56-1/42-1/30-1/20-1/12-1/6-1/2

= 9/10 -( 1/90 + 1/72 + ... + 1/2) 
= 9/10 - { 1/( 9.10) + 1/(9.8) + ... + 1/( 2.1)} 
= 9/10 - ( 1/9 - 1/10 + 1/8 - 1/9 + ...+ 1 - 1/2) ( 1/90 = 1/(9.10) = 1/9 - 1/10) 
= 9/10 - ( 1 - 1/10) 
= 9/10 - 9/10

= 0

9/10-1/90-1/72-1/56-1/42-1/30-1/20-1/12-1/6-1/2

=9/10-(1/9*10+1/8*9+...+1/1*2)

=9/10-(1/9-1/10+...+1-1/2)

=9/10-(-1/10+1)=9/10-9/10=0

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

\(=\dfrac{9}{10}-\left(\dfrac{1}{2}+\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{20}+...+\dfrac{1}{72}+\dfrac{1}{90}\right)\)

\(=\dfrac{9}{10}-\left(\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+\dfrac{1}{4.5}+...+\dfrac{1}{8.9}+\dfrac{1}{9.10}\right)\)

\(=\dfrac{9}{10}-\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{8}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{10}\right)\)

\(=\dfrac{9}{10}-\left(1-\dfrac{1}{10}\right)=\dfrac{9}{10}-\dfrac{9}{10}=0\)

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

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

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

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

\(=-\left(-\dfrac{9}{10}+1-\dfrac{1}{10}\right)=-\left(-\dfrac{9}{10}+\dfrac{9}{10}\right)=0\)

Ta có :

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

\(=\dfrac{9}{10}-\left(\dfrac{1}{90}+\dfrac{1}{72}+\dfrac{1}{56}+\dfrac{1}{42}+\dfrac{1}{30}+\dfrac{1}{20}+\dfrac{1}{12}+\dfrac{1}{6}+\dfrac{1}{2}\right)\)

\(=\dfrac{9}{10}-\left(\dfrac{1}{9.10}+\dfrac{1}{9.8}+\dfrac{1}{7.6}+\dfrac{1}{6.5}+\dfrac{1}{5.4}+\dfrac{1}{4.3}+\dfrac{1}{3.2}+\dfrac{1}{2.1}\right)\)

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

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

\(=\dfrac{9}{10}-\dfrac{9}{10}=0\)

=9/10-(1/2+1/6+...+1/90)

=9/10-(1-1/2+1/2-1/3+...+1/9-1/10)

=9/10-9/10=0

em lớp 6  nha

B= 1/2 + 1/6 + 1/12 +1/20 + 1/30 + 1/42 + 1/56 + 1/72

B= 1/1*2 + 1/2*3 + 1/3*4 + 1/4*5 + 1/5*6 + 1/6*7 + 1/7*8 + 1/8*9

B=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8+1/8-1/9

B=1+0-0-0-0-0-0-0-1/9

B=1-1/9

B=8/9

k em nha

phần A em chịu

còn câu dưới đó e

\(1\frac{1}{2}+2\frac{1}{6}+3\frac{1}{12}+4\frac{2}{20}+5\frac{1}{30}+6\frac{1}{42}+7\frac{1}{56}+8\frac{1}{72}+9\frac{1}{90}+\frac{1}{10}\)\(=\frac{3}{2}+\frac{13}{6}+\frac{37}{12}+\frac{81}{20}+\frac{151}{30}+\frac{253}{42}+\frac{393}{56}+\frac{577}{72}+\frac{811}{90}+\frac{1}{10}=46\)

k nha

๖ۣۜH๖ۣۜU๖ۣۜY  ๖ۣۜR๖ۣۜI๖ۣۜO

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

( 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 ) + ( 12 +16 +112 +120 +130 +142 +156 +172 +190 +110 )

= 45 + (16 +130 )+12 +112 +120 +142 +156 +172 +190 +110 

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

= 45 + (15 +120 )+12 +112 +142 +156 +172 +190 +110 

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

= 45 + (14 +12 )+112 +142 +156 +172 +190 +110 

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

= 45 + (34 +112 )+142 +156 +172 +190 +110 

rút gọn lại ta được 5 / 6 

= 45 + (56 +142 )+156 +172 +190 +110 

rút gọn tối giản ra 6 / 7

= 45 + (67 +156 )+172 +190 +110 

sau khi tính trong ngoặc rút gọn được 7 / 8

= 45 + (78 +172 )+190 +110 

tính trong ngoặc rồi rút gọn ra 8 / 9 

= 45 + (89 +190 )+110 

cũng rút gọn tiếp ta được 9 / 10

= 45 + (910 +110 )

= 45 + 1

= 46

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

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

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

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