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25 tháng 7 2015
Cho tg tren la A
A=\(\frac{1}{4}+\frac{1}{12}+\frac{1}{24}+\frac{1}{40}+\frac{1}{60}+\frac{1}{84}\)
\(A=2\left(\frac{1}{2.4}+\frac{1}{4.6}+\frac{1}{6.8}+\frac{1}{8.10}+\frac{1}{10.12}+\frac{1}{12.14}\right)\)
\(A=2\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+\frac{1}{8}-\frac{1}{10}+\frac{1}{10}-\frac{1}{12}+\frac{1}{12}-\frac{1}{14}\right)\)
\(A=2\left(\frac{1}{2}-\frac{1}{14}\right)\)
\(A=2.\frac{3}{7}\)
\(A=\frac{6}{7}\)
ND
1
25 tháng 7 2015
Ta co :
\(\frac{1}{4}+\frac{1}{12}+\frac{1}{24}+\frac{1}{40}+\frac{1}{60}+\frac{1}{84}\)
\(=2\left(\frac{1}{2.4}+\frac{1}{4.6}+\frac{1}{6.8}+\frac{1}{8.10}+\frac{1}{10.12}+\frac{1}{12.14}\right)\)
\(=2\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+\frac{1}{8}-\frac{1}{10}+\frac{1}{10}-\frac{1}{12}+\frac{1}{12}-\frac{1}{14}\right)\)
\(=2\left(\frac{1}{2}-\frac{1}{14}\right)\)
\(=2.\frac{3}{7}\)
\(=\frac{6}{7}\)
25 tháng 7 2015
Đặt A = 1/4 + ... +1/84
A = 2/8 + 2/24 + ... + 2/168
A = 2/2.4 + 2/4.6 + ... + 2/12.14
A = 1/2 - 1/4 + 1/4 - 1/6 + .. + 1/12 - 1/14
A = 1/2 - 1/14
A = 6/14 = 3/7
25 tháng 7 2015
\(A=\frac{1}{4}+\frac{1}{12}+\frac{1}{24}+\frac{1}{40}+\frac{1}{60}+\frac{1}{84}\)
\(A=\frac{2}{8}+\frac{2}{24}+\frac{2}{48}+\frac{2}{80}+\frac{2}{120}+\frac{2}{168}\)
\(A=\frac{2}{2.4}+\frac{2}{4.6}+\frac{2}{6.8}+\frac{2}{8.10}+\frac{2}{10.12}+\frac{2}{12.14}\)
\(A=\left(\frac{1}{2}-\frac{1}{4}\right)+\left(\frac{1}{4}-\frac{1}{6}\right)+\left(\frac{1}{6}-\frac{1}{8}\right)+\left(\frac{1}{8}-\frac{1}{10}\right)+\left(\frac{1}{10}-\frac{1}{12}\right)+\left(\frac{1}{12}-\frac{1}{14}\right)\)
\(A=\frac{1}{2}-\frac{1}{14}\)
\(A=\frac{3}{7}\)
Vậy \(\frac{1}{4}+\frac{1}{12}+\frac{1}{24}+\frac{1}{40}+\frac{1}{60}+\frac{1}{84}=\frac{3}{7}\)
13 tháng 3 2020
+) \(M=\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+....+\frac{1}{2019\cdot2020}\)
\(M=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+.....+\frac{1}{2019}-\frac{1}{2010}\)
\(M=1-\frac{1}{2010}=\frac{2009}{2010}\)
Vậy M=\(\frac{2009}{2010}\)
+) Đặt A=\(\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)\cdot\cdot\cdot\cdot\cdot\left(1-\frac{1}{50}\right)\)
\(A=\frac{1}{2}\cdot\frac{2}{3}\cdot\cdot\cdot\cdot\frac{49}{50}\)
\(A=\frac{1\cdot2\cdot\cdot\cdot\cdot49}{2\cdot3\cdot\cdot\cdot\cdot50}=\frac{1}{50}\)
NV
0
SU
1
NH
1
DD
Đoàn Đức Hà
Giáo viên
4 tháng 3 2022
\(\frac{1}{1+2}+\frac{1}{1+2+3}+...+\frac{1}{1+2+...+20}\)
\(=\frac{2}{2\times3}+\frac{2}{3\times4}+...+\frac{2}{20\times21}\)
\(=2\times\left(\frac{1}{2\times3}+\frac{1}{3\times4}+...+\frac{1}{20\times21}\right)\)
\(=2\times\left(\frac{3-2}{2\times3}+\frac{4-3}{3\times4}+...+\frac{21-20}{20\times21}\right)\)
\(=2\times\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{20}-\frac{1}{21}\right)\)
\(=2\times\left(\frac{1}{2}-\frac{1}{21}\right)\)
\(=\frac{19}{21}\)
TT
1
12 tháng 3 2018
BÀI 1:
\(S=1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}\)
\(S=1+\frac{1}{1.2}+\frac{1}{2.2}+\frac{1}{2.4}+\frac{1}{4.4}+\frac{1}{4.8}\)
\(S=1+1-\frac{1}{2}+\frac{1}{2}-\frac{1}{2}+\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{4}+\frac{1}{4}-\frac{1}{8}\)
\(S=1+1-\frac{1}{8}\)
\(S=\frac{15}{8}\)
BÀI 2:
\(A=1.2+2.3+3.4+...+98.99\)
\(\Rightarrow3A=1.2.3+2.3.3+3.4.3+...+98.99.3\)
\(3A=1.2.\left(3-0\right)+2.3.\left(4-1\right)+3.4.\left(5-2\right)+...+98.99.\left(100-97\right)\)
\(3A=1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+...+98.99.100-97.98.99\)
\(3A=\left(1.2.3+2.3.4+3.4.5+98.99.100\right)-\left(1.2.3+2.3.4+...+97.98.99\right)\)
\(3A=98.99.100\)
\(3A=970200\)
\(\Rightarrow A=970200:3\)
\(A=323400\)
CHÚC BN HỌC TỐT!!!
9 tháng 4 2020
a) Ta có:
1/( 2.3 ) = ( 3 - 2 )/( 2.3 )
= 3/( 2.3 ) - 2/( 2.3 )
= 1/2 - 1/3.
1/( 3.4 ) = ( 4 - 3 )/( 3.4 )
= 4/( 3.4 ) - 3/( 3.4 )
= 1/3 - 1/4.
b)
Ta có:
A = 1/( 5.6 ) + 1/( 6.7 ) + 1/( 7.8 ) + ..... + 1/( 2019.2020 )
A = 1/5 - 1/6 + 1/6 - 1/7 + 1/7 - 1/8 + ..... + 1/2019 - 1/2020
A = 1/5 - 1/2020
A = 403/2020
Vậy A = 403/2020.
NN
9 tháng 4 2020
a) Ta có: \(\frac{1}{2.3}=\frac{3-2}{2.3}=\frac{3}{2.3}-\frac{2}{2.3}=\frac{1}{2}-\frac{1}{3}\)
\(\frac{1}{3.4}=\frac{4-3}{3.4}=\frac{4}{3.4}-\frac{3}{3.4}=\frac{1}{3}-\frac{1}{4}\)
b) Ta có: \(A=\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}+.......+\frac{1}{2019.2020}\)
\(=\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+........+\frac{1}{2019}-\frac{1}{2020}\)
\(=\frac{1}{5}-\frac{1}{2020}=\frac{403}{2020}\)
CU
11 tháng 2 2019
A = (-1)(-1)^2(-1)^3...(-1)^2019
A = (-1)^1+2+3+...+2019
A = (-1)^2039190
A = 1
S = 1.2.3 + 2.3.4 + 3.4.5 + ... + 2018.2019.2020
4S = 1.2.3.4 + 2.3.4.4 + 3.4.5.4 + .... + 2018.2019.2020.4
4S = 1.2.3.4 + 2.3.4.(5 - 1) + 3.4.5.(6 - 2) + ... + 2018.2019.2020.(2021 - 2017)
4S = 1.2.3.4 + 2.3.4.5 - 1.2.3.4 + 3.4.5.6 - 2.3.4.5 + ... + 2018.2019.2020.2021 - 2017.2018.2019
4S = 2018.2019.2020.2021
S = 2018.2019.2020.2021 : 4 = ...
=999999
999999.1-1\1=999999