So sánh A và B :
A=\(\dfrac{1}{1.2}\) . \(\dfrac{4}{2.3}\) . \(\dfrac{9}{3.4}\) . \(\dfrac{16}{4.5}\) ... \(\dfrac{2500}{50.51}\) và B=\(\dfrac{13}{150}\)
LÀm giúp em với ạ . ai làm đc em tick ạ!
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
15 tháng 4 2023
a: \(=\dfrac{1}{1\cdot2}-\dfrac{1}{2\cdot3}+\dfrac{1}{2\cdot3}-\dfrac{1}{3\cdot4}+...+\dfrac{1}{18\cdot19}-\dfrac{1}{19\cdot20}\)
=1/2-1/380
=179/380
b: \(=\dfrac{1}{1\cdot3}-\dfrac{1}{3\cdot5}+\dfrac{1}{3\cdot5}-\dfrac{1}{5\cdot7}+...+\dfrac{1}{21\cdot23}-\dfrac{1}{23\cdot25}\)
\(=\dfrac{1}{3}-\dfrac{1}{575}=\dfrac{572}{1725}\)
c: \(=1+\dfrac{1}{2}-\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{19}+\dfrac{1}{20}-\dfrac{1}{20}-\dfrac{1}{21}\)
=1-1/21
=20/21
d: \(=\left(1-\dfrac{1}{9}\right)\left(1-\dfrac{1}{16}\right)\cdot...\cdot\left(1-\dfrac{1}{121}\right)\)
\(=\dfrac{2}{3}\cdot\dfrac{3}{4}\cdot...\cdot\dfrac{10}{11}\cdot\dfrac{3}{2}\cdot\dfrac{4}{3}\cdot...\cdot\dfrac{12}{11}\)
\(=\dfrac{2}{11}\cdot\dfrac{12}{2}=\dfrac{12}{11}\)
8 tháng 10 2021
a) Áp dụng t/c dtsbn:
\(\dfrac{x}{7}=\dfrac{y}{13}=\dfrac{x+y}{7+13}=\dfrac{40}{20}=2\)
\(\Rightarrow\left\{{}\begin{matrix}x=2.7=14\\y=2.13=26\end{matrix}\right.\)
b) \(\dfrac{3}{x}=\dfrac{7}{y}\Rightarrow\dfrac{x}{3}=\dfrac{y}{7}\)
Và \(x+16=y\Rightarrow y-x=16\)
Áp dụng t/c dtsbn:
\(\dfrac{x}{3}=\dfrac{y}{7}=\dfrac{y-x}{7-3}=\dfrac{16}{4}=4\)
\(\Rightarrow\left\{{}\begin{matrix}x=4.3=12\\y=4.7=28\end{matrix}\right.\)
ML
2
LT
Lương Thị Vân Anh
CTVHS
26 tháng 4 2023
\(A=\dfrac{1}{1\cdot2}+\dfrac{1}{2\cdot3}+\dfrac{1}{3\cdot4}+...+\dfrac{1}{19\cdot20}\)
\(=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{19}-\dfrac{1}{20}\)
\(=1-\dfrac{1}{20}=\dfrac{19}{20}\)
BD
26 tháng 4 2023
\(A=\dfrac{1}{1\cdot2}+\dfrac{1}{2\cdot3}+\dfrac{1}{3\cdot4}+\dfrac{1}{4\cdot5}+....+\dfrac{1}{19\cdot20}\)
\(A=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+....+\dfrac{1}{19}-\dfrac{1}{20}\)
\(A=1-\dfrac{1}{20}\)
\(A=\dfrac{19}{20}\)
VD
20 tháng 3 2022
d, `3,15+2,4=5,55`
e, \(\dfrac{5}{7}.\dfrac{2}{11}+\dfrac{5}{7}.\dfrac{9}{11}=\dfrac{5}{7}\left(\dfrac{2}{11}+\dfrac{9}{11}\right)=\dfrac{5}{7}.\dfrac{11}{11}=\dfrac{5}{7}.1=\dfrac{5}{7}\)
f, `1,25.3,6+3,6.8,75=3,6(1,25+8,75)=3,6.10=36`
\(h,\dfrac{1}{1.2}+\dfrac{1}{2.3}+...+\dfrac{1}{99.100}\\ =1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{99}-\dfrac{1}{100}\\ =1-\dfrac{1}{100}\\ =\dfrac{99}{100}\)
20 tháng 3 2022
\(e\dfrac{5}{7}\times\left(\dfrac{2}{11}+\dfrac{9}{11}\right)=\dfrac{5}{7}\times1=\dfrac{5}{7}\)
\(f3.6\times\left(1.25+8.75\right)=3.6\times10=36\)
DT
6
26 tháng 4 2017
Nhận xét thấy:
\(\dfrac{1}{1.2}\)= 1-\(\dfrac{1}{2}\); \(\dfrac{1}{2.3}=\dfrac{1}{2}-\dfrac{1}{3}\);...
Ta có
A= 1-\(\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}\)
A= 1- \(\dfrac{1}{6}\)
A= \(\dfrac{5}{6}\)
Vậy A= \(\dfrac{5}{6}\)
26 tháng 4 2017
CAU NAY RAT DE NHA BAN
A=\(\dfrac{1}{1}\)-\(\dfrac{1}{2}\)+\(\dfrac{1}{2}\)-\(\dfrac{1}{3}\)+\(\dfrac{1}{4}\)-\(\dfrac{1}{5}\)+\(\dfrac{1}{5}\)-\(\dfrac{1}{6}\)
A=1-\(\dfrac{1}{6}\)
=>A=\(\dfrac{5}{6}\)
DD
4
KS
5 tháng 4 2022
\(\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+\dfrac{1}{4.5}\)
=\(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}\)
=\(1-\dfrac{1}{5}\)
=\(\dfrac{4}{5}\)
18 tháng 4 2021
Sửa đề : a, \(S=\dfrac{3}{1.2}+\dfrac{3}{2.3}+\dfrac{3}{3.4}+\dfrac{3}{4.5}+...+\dfrac{3}{2015.2016}\)
\(=3\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-...+\dfrac{1}{2015}-\dfrac{1}{2016}\right)\)
\(=3\left(\dfrac{2016-1}{2016}\right)=3.\dfrac{2015}{2016}=\dfrac{6045}{2016}\)
18 tháng 4 2021
Câu a) sửa đề: 3/5015.2016 ➜ 3/2015.2016
Giải:
a) S=3/1.2 + 3/2.3 + 3/3.4 +3/4.5 +...+ 3/2015.2016
S=3.(1/1.2 + 1/2.3 + 1/3.4 + 1/4.5 +...+ 1/2015.2016)
S=3.(1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+...+1/2015-1/2016)
S=3.(1-1/2016)
S=3. 2015/2016
S=2015/672
b) Mk chưa biết làm nên bạn tự suy nghĩ nhé, xin lỗi!
NT
Nguyễn Thị Thương Hoài
Giáo viên
VIP
19 tháng 3
A = \(\dfrac{3}{4}\).\(\dfrac{8}{9}\).\(\dfrac{15}{16}.\)\(\dfrac{24}{25}\)...\(\dfrac{9800}{9801}\)
A = \(\dfrac{1.3}{2.2}\).\(\dfrac{2.4}{3.3}\).\(\dfrac{3.5}{4.4}\)...\(\dfrac{98.100}{99.99}\)
A = \(\dfrac{1}{2}.\dfrac{100}{99}\)
A = \(\dfrac{50}{99}\)
B = \(\dfrac{1.2+2.3+3.4+...+98.99}{98.99.100}\)
Đặt tử số là C Thì
C = 1.2 + 2.3 + 3.4 +...+ 98.99
C = \(\dfrac{1}{3}\).(1.2.3 + 2.3.3 + 3.4.3 + ...+ 98.99.3)
C = \(\dfrac{1}{3}\).[1.2.3 + 2.3.(4-1) + 3.4.(5-2) +...+ 98.99.(100-97)]
C = \(\dfrac{1}{3}\).[1.2.3 -1.2.3+2.3.4- 2.3.4 + 2.4.5 - .... - 97.98.99 + 98.99.100]
C = \(\dfrac{1}{3}\).98.99.100
B = \(\dfrac{\dfrac{1}{3}.98.99.100}{98.99.100}\)
B = \(\dfrac{1}{3}\) = \(\dfrac{33}{99}\) < \(\dfrac{50}{99}\) = A
Vậy B < A
\(A=\dfrac{1}{2}.\dfrac{2}{3}.\dfrac{3}{4}.\dfrac{4}{5}.....\dfrac{50}{51}=\dfrac{1}{51}=\dfrac{3}{153}< \dfrac{3}{150}< \dfrac{13}{150}\)
\(\Rightarrow A< B\)
Ta có
\(A=\dfrac{1}{1\cdot2}\cdot\dfrac{4}{2\cdot3}\cdot\dfrac{9}{3\cdot4}\cdot\dfrac{16}{4\cdot5}..\cdot\dfrac{2500}{50\cdot51}\)
\(A=\dfrac{1^2}{1\cdot2}\cdot\dfrac{2^2}{2\cdot3}\cdot\dfrac{3^2}{3\cdot4}\cdot\dfrac{4^2}{4\cdot5}+...+\dfrac{50^2}{50\cdot51}\)
\(A=\dfrac{1^2\cdot2^2\cdot3^2\cdot...\cdot50^2}{1\cdot2\cdot2\cdot3\cdot3\cdot4\cdot4\cdot5\cdot..\cdot50\cdot51}\)
\(A=\dfrac{1^2\cdot2^2\cdot3^2\cdot...\cdot50^2}{1\cdot2^2\cdot3^2\cdot4^2\cdot...\cdot50^2\cdot51}\)\(=\dfrac{1}{51}\)
Có \(A=\dfrac{1}{51}=\dfrac{13}{663}< B=\dfrac{13}{150}\)