Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
\(\frac{1}{2011}.x=\left(1-\frac{1}{2}\right).\left(1-\frac{1}{3}\right).\left(1-\frac{1}{4}\right)....\left(1-\frac{1}{2010}\right).\left(1-\frac{1}{2011}\right)\)
\(\frac{1}{2011}.x=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}....\frac{2009}{2010}.\frac{2010}{2011}\)
\(\frac{1}{2011}.x=\frac{1.2.3...2009.2010}{2.3.4...2010.2011}\)\(=\frac{1}{2011}\)
\(x=\frac{1}{2011}:\frac{1}{2011}=1\)
Vậy x=1
\(\frac{1}{2011}.x=\frac{1}{2}.\left(\frac{2}{3}\right).\left(\frac{3}{4}\right)......\left(\frac{2010}{2011}\right)\)
\(\frac{1}{2011}.x=\frac{2}{4}.\left(\frac{4}{6}\right).\left(\frac{6}{8}\right).......\left(\frac{4018}{4020}\right).\left(\frac{4020}{4022}\right)\)
\(\frac{1}{2011}.x=\frac{2.4.6.8.....4018.4020}{4.6.8.10.....4020.4022}\)
\(\frac{1}{2011}.x=\frac{2}{4022}\)
\(\Rightarrow\)\(x=\frac{2}{4022}:\frac{1}{2011}=1\)
Ai thấy đún thì ủng hộ mink nha !!!
Thanks you very much !!
Chúc các bạn luôn học giỏi !!!
a) \(=\frac{3}{2}.\frac{4}{3}....\frac{100}{99}=\frac{100}{2}=50\)
a) =3/2 . 4/3 . 5/4 ...100/99
=\(\frac{3.4.5...100}{2.3.4..99}\)
=\(\frac{100}{2}\)
b) =
\(M=\left[\frac{1}{2}-1\right]\cdot\left[\frac{1}{3}-1\right]\cdot\left[\frac{1}{4}-1\right]\cdot...\cdot\left[\frac{1}{2011}-1\right]\)
\(M=\left[\frac{1}{2}-\frac{2}{2}\right]\cdot\left[\frac{1}{3}-\frac{3}{3}\right]\cdot\left[\frac{1}{4}-\frac{4}{4}\right]\cdot...\cdot\left[\frac{1}{2011}-\frac{2011}{2011}\right]\)
\(M=\frac{-1}{2}\cdot\frac{-2}{3}\cdot\frac{-3}{4}\cdot...\cdot\frac{-2010}{2011}\)
\(M=\frac{\left[-1\right]\cdot\left[-2\right]\cdot\left[-3\right]\cdot...\cdot\left[-2010\right]}{2\cdot3\cdot4\cdot...\cdot2011}\)
\(M=\frac{1\cdot2\cdot3\cdot...\cdot2010}{2\cdot3\cdot4\cdot...\cdot2011}=\frac{1}{2011}\)
B
từ 1 đến 2012 có tất cả:
2012-1:1+1 = 2012 (số)
=>có: 2012:2 = 1006 (cặp)
Mà mỗi cặp bằng (-1)nên
tổng dãy số trên là: 1006 . (-1) = -1006
(1-2)+(2-3)+(3-4)+(5-6)+...+(2011-2012)
=-1+(-1)+(-1)+(-1)+...+(-1)
có tất cả các số -1 trên dãy số trên là
(2012-2);2+1=1006
vậy suy ra ; -1x1006=(-1006)
chac chan la dung
\(\left(1-\frac{1}{2}\right).\left(1-\frac{1}{3}\right).\left(1-\frac{1}{4}\right)...........\left(1-\frac{1}{19}\right).\left(1-\frac{1}{20}\right)\)
\(=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}.............\frac{18}{19}.\frac{19}{20}\)
\(=\frac{1.2.3...........18.19}{2.3.4...................19.20}=\frac{1.\left(2.3.4..........18.19\right)}{\left(2.3.............19\right).20}=\frac{1}{20}\)
\(D=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}.....\frac{998}{999}.\frac{999}{1000}\)
\(D=\frac{1}{1000}\)( rút gọn những thừa số giống nhau ở tử và mẫu)
Vậy \(D=\frac{1}{1000}\)
D = \(\frac{1}{2}\times\frac{2}{3}\times...\times\frac{999}{1000}\)
D = \(\frac{1}{1000}\)
\(A=\left(1-\frac{2}{5}\right)\left(1-\frac{2}{7}\right)\left(1-\frac{2}{9}\right)\cdot\cdot\cdot\left(1-\frac{2}{2011}\right)\)
\(A=\left(\frac{5-2}{5}\right)\left(\frac{7-2}{7}\right)\left(\frac{9-2}{9}\right)\cdot\cdot\cdot\left(\frac{2011-2}{2011}\right)\)
\(A=\frac{3}{5}\cdot\frac{5}{7}\cdot\frac{7}{9}\cdot\cdot\cdot\frac{2009}{2011}\)(các thừa số trên tử giống dưới mẫu mình lượt bỏ đi nhé!)
\(A=\frac{3}{2011}\)
\(A=\left(1-\frac{2}{5}\right)\left(1-\frac{2}{7}\right)\left(1-\frac{2}{9}\right)...\left(1-\frac{2}{2011}\right)\)
\(=\frac{3}{5}.\frac{5}{7}.\frac{7}{9}...\frac{2009}{2011}\)
\(=\frac{3}{2011}\)
\(\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)\left(1-\frac{1}{4}\right)...\left(1-\frac{1}{2011}\right)=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}...\frac{2010}{2011}=\frac{1}{2011}\)
(1-1/2)(1-1/3)........(1-1/2011)
=1//2*2/3*3/4*....*2010/2011
=1/2011