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T
3
CL
6 tháng 7 2015
ta có :
= ( 1 + 59049 ) + ( 3 + 2187 ) + ( 9 + 6561 ) + ( 27 + 243 ) + ( 81 + 729 )
= 59050 + 2190 + 6570 + 270 + 810
= 59050 + ( 2190 + 810 ) + 6570 + 270
= 59050 + 3000 + 6570 + 270
= 59050 + ( 3000 + 6570 ) + 270
= 59050 + 9570 + 270
= 68620 + 270
= 68890
TD
2
28 tháng 8 2014
lấy MS chung là 2187, ta có:
729 + 243 + 81 + 9 + 3 + 1
________________________ = 1066/2187
2187
16 tháng 9 2018
\(A=\frac{1}{2}+\frac{1}{4}+...+\frac{1}{2048}\)
\(A=\left(1-\frac{1}{2}\right)+\left(\frac{1}{2}-\frac{1}{4}\right)+...+\left(\frac{1}{1024}-\frac{1}{2048}\right)\)
\(A=1-\frac{1}{2048}\)
\(\Rightarrow\)\(A=\frac{2047}{2048}\)
\(3B=1+\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}+\frac{1}{243}+\frac{1}{729}\)
\(3B-B=1-\frac{1}{2187}\)
\(2B=\frac{2186}{2187}\)
\(\Rightarrow B=\frac{2186}{4374}=\frac{1093}{2187}\)
NP
3
NT
Nguyễn Thị Thương Hoài
Giáo viên
VIP
1 tháng 12 2023
A = \(\dfrac{1}{2}\) + \(\dfrac{1}{4}\) + \(\dfrac{1}{8}\) + \(\dfrac{1}{16}\) + \(\dfrac{1}{32}\)
2 \(\times\) A = 1 + \(\dfrac{1}{2}\) + \(\dfrac{1}{4}\) + \(\dfrac{1}{8}\) + \(\dfrac{1}{16}\)
2 \(\times\) A - A = 1 + \(\dfrac{1}{2}\) + \(\dfrac{1}{4}\) + \(\dfrac{1}{8}\) + \(\dfrac{1}{16}\) - (\(\dfrac{1}{2}\) + \(\dfrac{1}{4}\) + \(\dfrac{1}{8}\) + \(\dfrac{1}{16}\) + \(\dfrac{1}{32}\))
A = 1 + \(\dfrac{1}{2}\) + \(\dfrac{1}{4}\) + \(\dfrac{1}{8}\) + \(\dfrac{1}{16}\) - \(\dfrac{1}{2}\) - \(\dfrac{1}{4}\) - \(\dfrac{1}{8}\) - \(\dfrac{1}{16}\) - \(\dfrac{1}{32}\)
A = 1 - \(\dfrac{1}{32}\)
A = \(\dfrac{31}{32}\)
LJ
9 tháng 11 2017
Ta có: \(B=\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}+\frac{1}{243}+\frac{1}{729}\)
\(\Rightarrow B=\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+\frac{1}{3^4}+\frac{1}{3^5}+\frac{1}{3^6}\)
\(\Rightarrow3B=1+\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+\frac{1}{3^4}+\frac{1}{3^5}\)
\(\Rightarrow3B-B=\left(1+\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^4}+\frac{1}{3^5}\right)-\left(\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+\frac{1}{3^4}+\frac{1}{3^5}+\frac{1}{3^6}\right)\)
\(\Rightarrow2B=1-\frac{1}{3^6}\)
\(\Rightarrow B=\frac{1-\frac{1}{3^6}}{2}\)
H9
HT.Phong (9A5)
CTVHS
1 tháng 4 2023
Chu vi của một mảnh đất hình vuông là 60m , người ta chia mảnh đất thành 4 mảnh đất hình vuông có diện tích bằng nhau . Vậy chu vi một mảnh đất là ......30.... m
Kết quả của biểu thức :
\(A=\dfrac{1}{3}+\dfrac{1}{9}+\dfrac{1}{27}+\dfrac{1}{81}+...+\dfrac{1}{2187}\)
\(3A=3\times\left(\dfrac{1}{3}+\dfrac{1}{9}+\dfrac{1}{27}+...+\dfrac{1}{2187}\right)\)
\(3A=1+\left(\dfrac{1}{3}+\dfrac{1}{9}+\dfrac{1}{81}+...+\dfrac{1}{729}\right)\)
\(3A-A=1+\left(\dfrac{1}{3}+\dfrac{1}{9}+...+\dfrac{1}{729}\right)-\left(\dfrac{1}{3}+\dfrac{1}{9}+...+\dfrac{1}{2187}\right)\)
\(A\left(3-1\right)=\dfrac{1}{3}+\dfrac{1}{9}+\dfrac{1}{81}+...+\dfrac{1}{729}-\dfrac{1}{3}-\dfrac{1}{9}-\dfrac{1}{81}-...-\dfrac{1}{2187}\)
\(2A=1-\dfrac{1}{2187}\)
\(A=\dfrac{2186}{2187}:2=\dfrac{1093}{2187}\)
12 tháng 6 2015
Gọi tong trên là A
\(A=\frac{1}{3}+\frac{1}{9}+\frac{1}{81}+\frac{1}{243}+\frac{1}{7129}+\frac{1}{2187}\)
\(3A=\frac{1}{3}+\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}+\frac{1}{729}\)
\(3A-A=\left(1+\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}+\frac{1}{243}+\frac{1}{729}\right)-\left(\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}+\frac{1}{243}+\frac{1}{729}+\frac{1}{2187}\right)\)
\(2A=1+\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}+\frac{1}{243}+\frac{1}{729}-\frac{1}{3}-\frac{1}{9}-\frac{1}{27}-\frac{1}{81}-\frac{1}{243}-\frac{1}{729}-\frac{1}{2187}\)
\(2A=1-\frac{1}{2187}\)
\(2A=\frac{2186}{2187}\)
\(A=\frac{2186}{2187}:2\)
\(A=\frac{1093}{2187}\)
Vậy tổng A = \(\frac{1093}{2187}\)
12 tháng 6 2015
\(3y=3\cdot\frac{1}{1}+3\cdot\frac{1}{3}+3\cdot\frac{1}{9}+...+3\cdot\frac{1}{729}+3\cdot\frac{1}{2187}\)
\(=3+\frac{1}{1}+\frac{1}{3}...+\frac{1}{729}\)
=> \(3y-y=3+\frac{1}{1}+\frac{1}{3}+..+\frac{1}{729}-\frac{1}{1}-\frac{1}{3}-...-\frac{1}{2187}\)
<=> 2y = 3- 1/2187
=> y = \(\frac{3-\frac{1}{2187}}{2}\)
Bạn ghi rõ câu hỏi ra đi.
dấu đâu?
Đặt biểu thức là A
A x 3 - A = ( 4/3 + .... + 4/2187) x 3 - 4/3 - ... - 4/2187
A X 2 = 4 + ... + 4/729 - 4/3 - ... - 4/2187
A X 2 = 4 - 4/2187
A X 2 = 8744/2187
A = 8744/2187 : 2 = 4372/2187
chúc bạn học tốt, tick cho mình nha
A = \(\dfrac{4}{3}\) + \(\dfrac{4}{9}\) + \(\dfrac{4}{27}\) + \(\dfrac{4}{81}\)+ \(\dfrac{4}{243}\) + \(\dfrac{4}{729}\) + \(\dfrac{4}{2187}\)
3 x A = 4 + \(\dfrac{4}{3}\) + \(\dfrac{4}{9}\) + \(\dfrac{4}{27}\) +\(\dfrac{4}{81}\) +\(\dfrac{4}{243}\) + \(\dfrac{4}{729}\)
3 x A - A = 4 + \(\dfrac{4}{3}\) +\(\dfrac{4}{9}+\) \(\dfrac{4}{27}\) + \(\dfrac{4}{81}+\)\(\dfrac{4}{243}\) + \(\dfrac{4}{729}\) - (\(\dfrac{4}{3}\)+\(\dfrac{4}{9}\)+\(\dfrac{4}{27}\) +\(\dfrac{4}{81}\)+\(\dfrac{4}{243}\)+\(\dfrac{4}{729}\)+\(\dfrac{4}{2187}\))
A x (3 - 1) = 4+\(\dfrac{4}{3}\)+\(\dfrac{4}{27}\)+\(\dfrac{4}{81}+\)\(\dfrac{4}{243}\)+\(\dfrac{4}{729}\)-\(\dfrac{4}{3}\)-\(\dfrac{4}{9}\)-\(\dfrac{4}{27}\)-\(\dfrac{4}{81}\)-\(\dfrac{4}{243}\)-\(\dfrac{4}{729}\)-\(\dfrac{4}{2187}\)
A x 2 = (4 - \(\dfrac{4}{2187}\))+(\(\dfrac{4}{3}\)-\(\dfrac{4}{3}\)) +(\(\dfrac{4}{9}\)-\(\dfrac{4}{9}\))+(\(\dfrac{4}{27}\)-\(\dfrac{4}{27}\)) + (\(\dfrac{4}{81}-\dfrac{4}{81}\))+(\(\dfrac{4}{243}\)-\(\dfrac{4}{243}\))+(\(\dfrac{4}{729}\)-\(\dfrac{4}{729}\))
A x 2 = 4 - \(\dfrac{4}{2187}\)
A = (4 - \(\dfrac{4}{2187}\)): 2
A = 2 - \(\dfrac{2}{2187}\)
A = \(\dfrac{4372}{2187}\)
tinh nhanh, dau la dau +