Tính:
A=\(\frac{1}{2}.1111-\frac{1}{3}.1111-\frac{1}{6}.1111\)
B=\(\frac{3}{4.6}+\frac{3}{6.8}+\frac{3}{8.10}+.....+\frac{3}{20.22}\)
K
Khách
Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
Những câu hỏi liên quan
VL
3
CT
2
13 tháng 8 2015
\(\frac{3}{4.6}+\frac{3}{6.8}+\frac{3}{8.10}+\frac{3}{10.12}+\frac{3}{12.14}\)
=\(3.\left(\frac{1}{4.6}+\frac{1}{6.8}+\frac{1}{8.10}+\frac{1}{10.12}+\frac{1}{12.14}\right)\)
=\(\frac{3}{2}.\left(\frac{2}{4.6}+\frac{2}{6.8}+\frac{2}{8.10}+\frac{2}{10.12}+\frac{2}{12.14}\right)\)
=\(\frac{3}{2}.\left(\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+\frac{1}{8}-\frac{1}{10}+\frac{1}{10}-\frac{1}{12}+\frac{1}{12}-\frac{1}{14}\right)\)
=\(\frac{3}{2}.\left(\frac{1}{4}-\frac{1}{14}\right)\)
=\(\frac{3}{2}.\left(\frac{7}{28}-\frac{2}{28}\right)\)
=\(\frac{3}{2}.\frac{5}{28}=\frac{15}{56}\)
4 tháng 5 2020
\(\sqrt[]{\frac{ }{ }\frac{ }{ }\hept{\begin{cases}\\\end{cases}}\hept{\begin{cases}\\\\\end{cases}}\orbr{\begin{cases}\\\end{cases}}^2}\)
19 tháng 9 2016
Giải:
Đặt \(\frac{a}{b}=\frac{c}{d}=k\Rightarrow a=bk,c=dk\)
a) Ta có:
\(\frac{11a+3b}{11c+3d}=\frac{11bk+3b}{11dk+3d}=\frac{b\left(11k+3\right)}{d\left(11k+3\right)}=\frac{b}{d}\) (1)
\(\frac{3a-11b}{3c-11d}=\frac{3bk-11b}{3dk-11d}=\frac{b\left(3k-11\right)}{d\left(3k-11\right)}=\frac{b}{d}\) (2)
Từ (1) và (2) suy ra \(\frac{11a+3b}{11c+3d}=\frac{3a-11b}{3c-11d}\) (đpcm)
b) Ta có:
\(\frac{1111c-99d}{9999c-11d}=\frac{1111dk-99d}{9999dk-11d}=\frac{d\left(1111k-99\right)}{d\left(9999k-11\right)}=\frac{1111k-99}{9999k-11}\) (1)
\(\frac{1111a-99b}{9999a-11b}=\frac{1111bk-99b}{9999bk-11b}=\frac{b\left(1111k-99\right)}{b\left(9999k-11\right)}=\frac{1111k-99}{9999k-11}\) (2)
Từ (1) và (2) suy ra \(\frac{1111c-99d}{9999c-11d}=\frac{1111a-99b}{9999a-11b}\) (đpcm)
LT
11 tháng 3 2020
\(B=\frac{3}{2.4}-\frac{5}{4.6}+\frac{7}{6.8}-\frac{9}{8.10}+...+\frac{2019}{2018.2020}\)
\(B=\frac{3}{2.1.2.2}-\frac{5}{2.2.2.3}+\frac{7}{2.3.2.4}-\frac{9}{2.4.2.5}+...+\frac{2019}{2.1009.2.1010}\)
\(B=\frac{1}{4.}.\left(\frac{3}{1.2}-\frac{5}{2.3}+\frac{7}{3.4}-\frac{9}{4.5}+...+\frac{2019}{1009.1010}\right)\)
\(B=\frac{1}{4.}.\left(\frac{3}{1}-\frac{3}{2}-\frac{5}{2}+\frac{5}{3}+\frac{7}{3}-\frac{7}{4}-\frac{9}{4}+\frac{9}{5}+...+\frac{2019}{1009}-\frac{2019}{1010}\right)\)
\(B=\frac{1}{4.}.\left(\frac{3}{1}-4+4-4+4-...+4-\frac{2019}{1010}\right)\)
\(B=\frac{1}{4.}.\left(\frac{3}{1}-\frac{2019}{1010}\right)=\frac{1011}{4040}\)
GL
\(\frac{3}{4}x-14\frac{2}{3}:\left(\frac{11}{15}+\frac{1111}{3535}+\frac{111111}{636363}\right)=12\)
4
18 tháng 9 2020
\(\frac{3}{4}x-14\frac{2}{3}:\left(\frac{11}{15}+\frac{1111}{3535}+\frac{111111}{636363}\right)=12\)
\(\frac{3}{4}x-\frac{44}{3}:\left(\frac{11}{15}+\frac{11}{35}+\frac{11}{63}\right)=12\)
\(\frac{3}{4}x-\frac{44}{3}:\frac{11}{9}=12\)
\(\frac{3}{4}x-12=12\)
\(\frac{3}{4}x=12+12\)
\(\frac{3}{4}x=24\)
\(x=24:\frac{3}{4}\)
\(x=32\)
vậy \(x=32\)
HH
4
3 tháng 9 2017
\(S=\frac{1}{2.4}+\frac{1}{4.6}+\frac{1}{6.8}+\frac{1}{8.10}\)
\(2S=\frac{2}{2.4}+\frac{2}{4.6}+\frac{2}{6.8}+\frac{2}{8.10}\)
\(2S=\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+...+\frac{1}{8}-\frac{1}{10}\)
\(2S=\frac{1}{2}-\frac{1}{10}\)
\(2S=\frac{2}{5}\)
\(S=\frac{2}{5}:2\)
\(S=\frac{1}{5}\)
HN
3 tháng 9 2017
S = \(\frac{1}{2.4}+\frac{1}{4.6}+\frac{1}{6.8}+\frac{1}{8.10}\)
=> 2S = \(\frac{2}{2.4}+\frac{2}{4.6}+\frac{2}{6.8}+\frac{2}{8.10}\)
=> 2S = \(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+\frac{1}{8}-\frac{1}{10}\)
=> 2S = \(\frac{1}{2}-\frac{1}{10}=\frac{5}{10}-\frac{1}{10}=\frac{4}{10}=\frac{2}{5}\)
=> S = \(\frac{2}{5}:2=\frac{2}{5}x\frac{1}{2}=\frac{1}{5}\)
\(B=\frac{3}{4.6}+\frac{3}{6.8}+\frac{3}{8.10}+...+\frac{3}{20.22}\)
\(=\frac{1}{4.6}+\frac{1}{6.8}+\frac{1}{8.10}+...+\frac{1}{20.22}\)
\(=\left(\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+...+\frac{1}{20}-\frac{1}{22}\right)\)
\(=\frac{1}{4}-\frac{1}{22}\)
\(=\frac{9}{44}\)
A = 1111 x ( 1/2 - 1/3 - 1/6 )
A = 1111 x 0 = 0
B = 3/4 x 6 + 3/6 x 8 + 3/8 x 10 + ... + 3/20 x 22
B = 3/2 ( 1/4 - 1/6 + 1/6 - 1/8 + ... + 1/20 - 1/22 )
B = 3/2 x ( 1/4 - 1/22 )
B = 3/2 x 9/44 = 27/88