1+2+3....+7
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NT
Nguyễn Thị Thương Hoài
Giáo viên
VIP
27 tháng 3
\(\left(\dfrac{5}{7}-\dfrac{7}{7}\right)-\left[0,2-\left(-\dfrac{2}{7}-\dfrac{1}{10}\right)\right]\)
=\(-\dfrac{2}{7}-\left[\dfrac{1}{5}+\dfrac{2}{7}+\dfrac{1}{10}\right]\)
=\(-\dfrac{2}{7}-\dfrac{1}{5}-\dfrac{2}{7}-\dfrac{1}{10}\)
=\(\left(-\dfrac{2}{7}-\dfrac{2}{7}\right)-\left(\dfrac{1}{5}+\dfrac{1}{10}\right)\)
=\(-\dfrac{4}{7}-\left(\dfrac{2}{10}+\dfrac{1}{10}\right)\)
=\(-\dfrac{4}{7}-\dfrac{3}{10}\)
=\(-\dfrac{40}{70}-\dfrac{21}{70}\)
=\(-\dfrac{61}{70}\)
NT
Nguyễn Thị Thương Hoài
Giáo viên
VIP
27 tháng 3
(3 - \(\dfrac{1}{4}\) + \(\dfrac{2}{3}\)) - (5 - \(\dfrac{1}{3}\) - \(\dfrac{5}{6}\)) - (6 - \(\dfrac{7}{4}\) - \(\dfrac{3}{2}\))
= 3 - \(\dfrac{1}{4}\) + \(\dfrac{2}{3}\) - 5 + \(\dfrac{1}{3}\) + \(\dfrac{5}{6}\) - 6 + \(\dfrac{7}{4}\) + \(\dfrac{3}{2}\)
= (3 - 5 - 6) + ( \(\dfrac{7}{4}\) - \(\dfrac{1}{4}\)) + (\(\dfrac{2}{3}\) + \(\dfrac{1}{3}\)) + \(\dfrac{3}{2}\) + \(\dfrac{5}{6}\)
= - 8 + \(\dfrac{3}{2}\) + 1 + \(\dfrac{3}{2}\) + \(\dfrac{5}{6}\)
= (- 8 + 1) + (\(\dfrac{3}{2}\) + \(\dfrac{3}{2}\)) + \(\dfrac{5}{6}\)
= -7 + 3 + \(\dfrac{5}{6}\)
= - 4 + \(\dfrac{5}{6}\)
= \(\dfrac{-19}{6}\)
NM
20 tháng 7 2023
a) -1/24 - [ 1/4 - ( 1/2 - 7/8 )]
= -1/24 - [ 1/4 +3/8 ]
= -1/24 - 5/8
= -2/3.
DT
20 tháng 7 2023
a) -1/24 - [ 1/4 - ( 1/2 - 7/8 )]
= -1/24 - [ 1/4 +3/8 ]
= -1/24 - 5/8
= -2/3.
DD
Đoàn Đức Hà
Giáo viên
4 tháng 7 2021
\(A=1+7+7^2+7^3+...+7^{2007}\)
\(7A=7+7^2+7^3+7^4+...+7^{2008}\)
\(7A-A=\left(7+7^2+7^3+7^4+...+7^{2008}\right)-\left(1+7+7^2+7^3+...+7^{2007}\right)\)
\(6A=7^{2008}-1\)
\(A=\frac{7^{2008}-1}{6}\)
Tương tự, \(B=\frac{4^{101}-1}{3},C=\frac{3^{101}-1}{2}\).
DD
Đoàn Đức Hà
Giáo viên
4 tháng 7 2021
\(D=7+7^3+7^5+7^7+...+7^{99}\)
\(7^2.D=7^3+7^5+7^7+7^9+...+7^{101}\)
\(\left(7^2-1\right)D=\left(7^3+7^5+7^7+7^9+...+7^{101}\right)-\left(7+7^3+7^5+7^7+...+7^{99}\right)\)
\(48D=7^{101}-7\)
\(D=\frac{7^{101}-7}{48}\)
Tương tự, \(E=\frac{2^{9011}-2}{3}\)
24 tháng 8 2023
5: \(=3-\dfrac{1}{4}+\dfrac{2}{3}-5+\dfrac{1}{3}+\dfrac{6}{5}-6+\dfrac{7}{4}-\dfrac{3}{2}\)
\(=3-5-6+\dfrac{-1}{4}+\dfrac{7}{4}+\dfrac{2}{3}+\dfrac{1}{3}+\dfrac{6}{5}-\dfrac{3}{2}\)
\(=-8+\dfrac{3}{2}+1+\dfrac{-3}{10}\)
\(=-7+\dfrac{15-3}{10}=-7+\dfrac{6}{5}=-\dfrac{29}{5}\)
6: \(=6-\dfrac{2}{3}+\dfrac{1}{2}-5-\dfrac{5}{3}+\dfrac{3}{2}-3+\dfrac{7}{3}-\dfrac{5}{2}\)
\(=6-5-3-\dfrac{2}{3}-\dfrac{5}{3}+\dfrac{7}{3}+\dfrac{1}{2}+\dfrac{3}{2}-\dfrac{5}{2}\)
\(=-2-\dfrac{1}{2}=-\dfrac{5}{2}\)
7: \(=\dfrac{5}{3}-\dfrac{3}{7}+9-2-\dfrac{5}{7}+\dfrac{2}{3}+\dfrac{8}{7}-\dfrac{4}{3}-10\)
\(=9-2-10+\dfrac{5}{3}+\dfrac{2}{3}-\dfrac{4}{3}+\dfrac{-3}{7}-\dfrac{5}{7}+\dfrac{8}{7}\)
=-3+1
=-2
8: \(=8-\dfrac{9}{4}+\dfrac{2}{7}+6+\dfrac{3}{7}-\dfrac{5}{4}-3-\dfrac{2}{4}+\dfrac{9}{7}\)
\(=8+6-3+\dfrac{2}{7}+\dfrac{3}{7}+\dfrac{9}{7}-1-\dfrac{2}{4}\)
\(=11+2-1-\dfrac{1}{2}\)
=11+1/2
=11,5
HA
2
3 tháng 10 2023
\(\dfrac{2}{7}:\dfrac{1}{4}-\dfrac{1}{7}=\dfrac{2}{7}x\dfrac{4}{1}-\dfrac{1}{7}=\dfrac{8}{7}-\dfrac{1}{7}=\dfrac{7}{7}=1\)
\(\dfrac{7}{11}x0+\dfrac{5}{9}:\dfrac{1}{2}=0+\dfrac{5}{9}x\dfrac{2}{1}=\dfrac{10}{9}\)
\(\left(\dfrac{3}{7}+\dfrac{1}{4}\right):\dfrac{3}{4}=\left(\dfrac{12}{28}+\dfrac{7}{28}\right)x\dfrac{4}{3}=\dfrac{19}{28}x\dfrac{4}{3}=\dfrac{19}{21}\)
\(\dfrac{4}{3}x\dfrac{1}{2}+\dfrac{7}{2}:\dfrac{1}{4}=\dfrac{4}{6}+\dfrac{7}{2}x\dfrac{4}{1}=\dfrac{2}{3}+\dfrac{14}{1}=\dfrac{2}{3}+14=14\dfrac{2}{3}=\dfrac{44}{3}\)
HL
1
DT
Đỗ Thanh Hải
CTVVIP
15 tháng 5 2017
Ta có
A = \(\dfrac{1+7+7^2+7^3+...+7^{11}}{1+7+7^2+7^3+...+7^{10}}\)
Đặt C = 1 + 7 + 72 + 73+...+711
7C = 7 + 72 + 73 + ... + 711 + 712
=> 6C = 712 - 1
C = \(\dfrac{7^{12}-1}{6}\)
Đặt D = 1 + 7 + 72 + 73+...+710
7D = 7 + 72 + 73 + ... + 710 + 711
=> 6D = \(7^{11}-1\)
D = \(\dfrac{7^{11}-1}{6}\)
=> A = \(\dfrac{\dfrac{7^{12}-1}{6}}{\dfrac{7^{11}-1}{6}}\)
A = \(\dfrac{7^{12}-1}{6}\) : \(\dfrac{7^{11}-1}{6}\)
A = \(\dfrac{7^{12}-1}{6}.\dfrac{6}{7^{11}-1}\)
A = \(\dfrac{7^{12}-1}{7^{11}-1}\) = 7, 000000003
Lại có:
B = \(\dfrac{1+3+3^2+3^3+...+3^{11}}{1+3+3^2+3^3+...+3^{10}}\)\
Đặt H = \(1+3+3^2+3^3+...+3^{11}\)
3H = \(3+3^2+3^3+...+3^{12}\)
=> 2H = \(3^{12}-1\)
H = \(\dfrac{3^{12}-1}{2}\)
Đặt Q = \(1+3+3^2+3^3+...+3^{10}\)
3Q = \(3+3^2+3^3+...+3^{10}+3^{11}\)
=> 2Q = \(3^{11}-1\)
Q = \(\dfrac{3^{11}-1}{2}\)
=> B = \(\dfrac{\dfrac{3^{12}-1}{2}}{\dfrac{3^{11}-1}{2}}\)
B = \(\dfrac{3^{12}-1}{2}:\dfrac{3^{11}-1}{2}\)
B = \(\dfrac{3^{12}-1}{2}.\dfrac{2}{3^{11}-1}\)
B = \(\dfrac{3^{12}-1}{3^{11}-1}\)
B = 3, 00001129
Vì 7, 000000003 > 3, 00001129
=> A > B
Vậy A > B
= 1 + 2 + 3+4+5+6+7 = 28
k mình nha
Số các số hạng tổng trên là : ( 7 - 1 ) : 1 + 1 = 7 ( số )
Tổng : ( 7 + 1 ) .7 : 2 = 28
Vậy tổng dãy trên là 28
K mk đi
mk nhanh nhất nha