Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
\(\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{20}+\dfrac{1}{30}\)
\(=\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}\)
\(=\dfrac{1}{2}-\dfrac{1}{6}\)
\(=\dfrac{1}{3}\)
misa
Đặt tên biểu thức là A ta có :
\(A=\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+....+\frac{1}{90}+\frac{1}{110}\)
\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+....+\frac{1}{10}-\frac{1}{11}\)
\(=\left(\frac{1}{2}-\frac{1}{11}\right)+\left(\frac{1}{3}-\frac{1}{3}\right)+.....+\left(\frac{1}{10}-\frac{1}{10}\right)\)
\(=\left(\frac{1}{2}-\frac{1}{11}\right)+0+......+0\)
\(=\frac{11}{22}-\frac{2}{22}=\frac{9}{22}\)
\(\frac{1}{2x3}+\frac{1}{3x4}+\frac{1}{4x5}+...+\frac{1}{10.11}\)
=\(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{10}-\frac{1}{11}\)
=\(\frac{1}{2}-\frac{1}{11}\)
=\(\frac{9}{22}\)
Sai đầu bài nhé, số cuối cùng phải là 110. Giải :
\(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{90}+\frac{1}{110}\)
= \(\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{9.10}+\frac{1}{10.11}\)
=\(\left(\frac{1}{2}-\frac{1}{3}\right)+\left(\frac{1}{3}-\frac{1}{4}\right)+...+\left(\frac{1}{10}-\frac{1}{11}\right)\)
=\(\left(\frac{1}{2}-\frac{1}{11}\right)+0+...+0\)
=\(\frac{9}{22}\)
Mình sửa đề 1 chút nha
\(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+........+\frac{1}{90}+\frac{1}{110}\)
\(=\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+.....+\frac{1}{9.10}+\frac{1}{10.11}\)
\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+.....+\frac{1}{9}-\frac{1}{10}+\frac{1}{10}-\frac{1}{11}\)
\(=\frac{1}{2}-\frac{1}{11}\)
\(=\frac{9}{22}\)
\(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+....+\frac{1}{90}+\frac{1}{110}\)
\(=\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+.....+\frac{1}{9.10}+\frac{1}{10.11}\)
\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+.......+\frac{1}{9}-\frac{1}{10}+\frac{1}{10}-\frac{1}{11}\)
\(=\frac{1}{2}-\frac{1}{11}\)
\(=\frac{9}{22}\)
\(=\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+....+\frac{1}{10\cdot11}\)
\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{10}\cdot-\frac{1}{11}\)
\(=\frac{1}{2}-\frac{1}{11}\)
\(=\frac{9}{22}\)
bài ý dễ ợt à bạn học toán nâng cao đúng ko mình bận học nâng cao lp 5 ko làm đc vì mẹ mình gọi sorry nha
\(\dfrac{1}{2}+\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{20}+....+\dfrac{1}{110}\)
\(=\dfrac{1}{1\times2}+\dfrac{1}{2\times3}+\dfrac{1}{3\times4}+\dfrac{1}{4\times5}+....+\dfrac{1}{10\times11}\)
\(=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+....+\dfrac{1}{10}-\dfrac{1}{11}\)
\(=1-\dfrac{1}{11}=\dfrac{10}{11}\)
b) 13/17 : 8/3 - 5/17 : 8/3
= ( 13/17 - 5/17 ) : 8/3
= 7/17 * 3/8
=21/136
c) 1/6 + 1/12 + 1/20 + 1/20
= (1/6 + 1/12) + (1/20 + 1/20)
= (2/12 + 1/12) + (1/20 + 1/20)
= 3/12 + 2/20
= 1/4 +2/20
= 5/20 + 2/20
= 7/20
\(b)\frac{13}{17}\div\frac{8}{3}-\frac{5}{17}\div\frac{8}{3}\)
\(=\left(\frac{13}{17}-\frac{5}{17}\right)\div\frac{8}{3}\)
\(=\frac{8}{17}\div\frac{8}{3}\)
\(=\frac{3}{17}\)
\(c)\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{20}\)
\(=\left(\frac{2}{12}+\frac{1}{12}\right)+\left(\frac{1}{20}+\frac{1}{20}\right)\)
\(=\frac{1}{4}+\frac{2}{20}\)
\(=\frac{5}{20}+\frac{2}{20}=\frac{7}{20}\)
\(\frac{1.3.5+2.6.10+4.12.20+7.21.35}{1.5.7+2.10.14+4.20.28+7.35.49}\)
\(=\frac{1.3.5\left(1+2+4+7\right)}{1.5.7\left(1+2+7+7\right)}=\frac{1.3.5}{1.5.7}=\frac{15}{35}=\frac{3}{7}\)
\(\frac{1\cdot3\cdot5+2\cdot6\cdot10+4\cdot12\cdot20+7\cdot21\cdot35}{1\cdot5\cdot7+2\cdot10\cdot14+4\cdot20\cdot28+7\cdot35\cdot49}\)
\(=\)\(\frac{1\cdot3\cdot5\cdot\left(1+2+4+7\right)}{1\cdot5\cdot7\cdot\left(1+2+7+7\right)}\)
\(=\frac{1\cdot3\cdot5}{1\cdot5\cdot7}\)\(=\frac{15}{35}=\frac{3}{7}\)
bn vội quá viết nhầm lun kìa
hj hj chúc bn làm bài tốt nha
: A = 1/6+1/12+1/20+1/30+.........+1/210
A = 1/2.3 + 1/3.4 + 1/4.5 + 1/5.6 + ... + 1/14.15
A = 1/2 - 1/3 + 1/3 - 1/4 + 1/4 - 1/5 + 1/5 - 1/6 + ... + 1/14 - 1/15
A = 1/2 - 1/15
A = 13/30
Ta có: 1/2= 1/1- 1/2
1/6= 1/2 - 1/3
1/12= 1/3- 1/4
...
1/30= 1/5 - 1/6
1/42= 1/6 - 1/7
Thay vào tổng kia: 1/2+1/6+...+1/30+1/42= 1/2 - 1/3 + 1/3 - 1/4 + ... + 1/5 - 1/6 + 1/6 - 1/7 = 1/2 - 1/7= 5/14
Chúc bạn học tốt. Thân!