GIÚP MÌNH LÀM BÀI TẬP HÈ VỚI CÁC BẠN ƠI!
Cho B=(1/4-1).(1/9-1).................(1/100-1).So sánh B với -11/21
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
6 tháng 6 2017
B = \(\left(\frac{1}{4}-1\right).\left(\frac{1}{9}-1\right)...\left(\frac{1}{100}-1\right)\)
B = \(\frac{-3}{4}.\frac{-8}{9}...\frac{-99}{100}\)
B = \(-\left(\frac{3}{4}.\frac{8}{9}...\frac{99}{100}\right)\)
B = \(-\left(\frac{1.3}{2.2}.\frac{2.4}{3.3}...\frac{9.11}{10.10}\right)\)
B = \(-\left(\frac{1.2...9}{2.3...10}.\frac{3.4...11}{2.3...10}\right)\)
B = \(-\left(\frac{1}{10}.\frac{11}{2}\right)\)
B = \(\frac{-11}{20}\)
Vì \(\frac{11}{20}>\frac{11}{21}\)nên \(\frac{-11}{20}< \frac{-11}{21}\)
Vậy \(B< \frac{-11}{21}\)
PN
10 tháng 5 2021
a,\(A=\frac{1}{5}+\frac{1}{5^2}+\frac{1}{5^3}+...+\frac{1}{5^{100}}\)
\(=>5A=1+\frac{1}{5}+\frac{1}{5^2}+...+\frac{1}{5^{99}}\)
\(=>5A-A=1-\frac{1}{5^{100}}=>A=\frac{1-\frac{1}{5^{100}}}{4}\)
b, Ta có \(1-\frac{1}{5^{100}}< 1=>\frac{1-\frac{1}{5^{100}}}{4}< \frac{1}{4}\)hay \(A< \frac{1}{4}\)
NH
8
XO
1 tháng 11 2020
\(B=\left(\frac{1}{4}-1\right)\left(\frac{1}{9}-1\right)...\left(\frac{1}{100}-1\right)=\frac{-3}{4}.\frac{-8}{9}...\frac{-99}{100}=-\frac{3.8...99}{4.9....100}\)
\(=-\frac{1.3.2.4...9.11}{2.2.3.3....10.10}=-\frac{\left(1.2...9\right).\left(3.4...11\right)}{\left(2.3...10\right).\left(2.3...10\right)}=-\frac{1.11}{10.2}=-\frac{11}{20}< -\frac{11}{21}\)
28 tháng 12 2023
B=(
4
1
−1)(
9
1
−1)...(
100
1
−1)=
4
−3
.
9
−8
...
100
−99
=−
4.9....100
3.8...99
=
−
1.3.2.4...9.11
2.2.3.3....10.10
=
−
(
1.2...9
)
.
(
3.4...11
)
(
2.3...10
)
.
(
2.3...10
)
=
−
1.11
10.2
=
−
11
20
<
−
11
21
=−
2.2.3.3....10.10
1.3.2.4...9.11
=−
(2.3...10).(2.3.
..10)
(1.2...9).(3.4...11)
=−
10.2
1.11
=−
20
11
<−
21
11
LB
2
HP
3 tháng 7 2016
\(B=\left(1-\frac{1}{4}\right)\left(1-\frac{1}{9}\right)\left(1-\frac{1}{16}\right).....\left(1-\frac{1}{100}\right)\)
\(=\frac{3}{4}.\frac{8}{9}.\frac{15}{16}...............\frac{99}{100}\)
\(=\frac{3.8.15......99}{4.9.16....100}=\frac{\left(1.3\right).\left(2.4\right).\left(3.5\right).......\left(9.11\right)}{\left(2.2\right).\left(3.3\right).\left(4.4\right)......\left(10.10\right)}\)
\(=\frac{\left(1.2.3.....9\right).\left(3.4.5......11\right)}{\left(2.3.4.....10\right).\left(2.3.4.......10\right)}=\frac{1}{10}.\frac{11}{2}=\frac{11}{20}< \frac{11}{21}\)
Vậy B<11/21
LB
0
29 tháng 6 2017
\(A=\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)\left(1-\frac{1}{4}\right).......\left(1-\frac{1}{19}\right)\left(1-\frac{1}{20}\right)\)
\(A=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}......\frac{18}{19}.\frac{19}{20}\)
\(A=\frac{1}{20}\)
29 tháng 6 2017
\(A=\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)\left(1-\frac{1}{4}\right)........\left(1-\frac{1}{19}\right)\left(1-\frac{1}{20}\right)\)
\(\Leftrightarrow A=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}...........\frac{18}{19}.\frac{19}{20}\)
\(\Leftrightarrow A=\frac{1}{20}>\frac{1}{21}\)
\(\Leftrightarrow A>\frac{1}{21}\)
\(B=\left(1-\frac{1}{4}\right)\left(1-\frac{1}{9}\right)................\left(1-\frac{1}{100}\right)\)
\(\Leftrightarrow B=\frac{3}{4}.\frac{8}{9}..................\frac{99}{100}\)
\(B=\frac{1.3}{2^2}.\frac{2.4}{3^2}................\frac{9.11}{50^2}\)
\(B=\frac{11}{50}< \frac{11}{21}\)
\(B=\left(\frac{1}{4}-1\right).\left(\frac{1}{9}-1\right)...\left(\frac{1}{100}-1\right)\)
\(B=\frac{-3}{4}.\frac{-8}{9}...\frac{-99}{100}\)
\(B=-\left(\frac{3}{4}.\frac{8}{9}...\frac{99}{100}\right)\)
\(B=-\left(\frac{1.3}{2.2}.\frac{2.4}{3.3}...\frac{9.11}{10.10}\right)\)
\(B=-\left(\frac{1.2...9}{2.3...10}.\frac{3.4...11}{2.3...10}\right)\)
\(B=-\left(\frac{1}{10}.\frac{11}{2}\right)\)
\(B=\frac{-11}{20}< \frac{-11}{21}\)
Vậy \(B< \frac{-11}{21}\)