1+5/4+5/8+5/16+5/32+5/64
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tính nhanh p/s 1+ 5/4 + 5/8 + 5/16 + 5/32 + 5/64
9 tháng 5 2023
b: A=1/3+1/9+...+1/3^10
=>3A=1+1/3+...+1/3^9
=>A*2=1-1/3^10=(3^10-1)/3^10
=>A=(3^10-1)/(2*3^10)
c: C=3/2+3/8+3/32+3/128+3/512
=>4C=6+3/2+...+3/128
=>3C=6-3/512
=>C=1023/512
d: A=1/2+...+1/256
=>2A=1+1/2+...+1/128
=>A=1-1/256=255/256
G
1
DD
Đoàn Đức Hà
Giáo viên
22 tháng 6 2021
\(12\left(5^2+1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)\left(5^{32}+1\right)\)
\(=\frac{1}{2}\left(5^2-1\right)\left(5^2+1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)\left(5^{32}+1\right)\)
\(=\frac{1}{2}\left(5^4-1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)\left(5^{32}+1\right)\)
\(=\frac{1}{2}\left(5^8-1\right)\left(5^8+1\right)\left(5^{16}+1\right)\left(5^{32}+1\right)\)
\(=\frac{1}{2}\left(5^{16}-1\right)\left(5^{16}+1\right)\left(5^{32}+1\right)\)
\(=\frac{1}{2}\left(5^{32}-1\right)\left(5^{32}+1\right)\)
\(=\frac{1}{2}\left(5^{64}-1\right)\)
25 tháng 11 2019
\(1+\frac{5}{4}+\frac{5}{8}+\frac{5}{16}+\frac{5}{32}+\frac{5}{64}\)
\(=\frac{64}{64}+\frac{80}{64}+\frac{40}{64}+\frac{20}{64}+\frac{10}{64}+\frac{5}{64}\)
\(=\frac{64+80+40+20+10+5}{64}\)
\(=\frac{219}{64}\)
\(=\frac{27}{8}\)
TN
25 tháng 11 2019
1+5/4+5/8+5/16+5/32+5/64
=1+5/4+5/8+5/16+5/32+5/64
=1+(5/4+5/8+5/16+5/32+5/64)
=1+[5x(1/4+1/8+1/16+1/32+1/64)]
A=1/4+1/8+1/16+1/32+1/64
2A=1/2+1/4+1/8+1/16+1/32
2A-A=(1/2+1/4+1/8+1/16+1/32)+(1/4+1/8+1/16+1/32+1/64)
A=1/2-1/64
A=31/64
1+[5x31/64]
=1+155/64
=219/64
6 tháng 7 2020
\(E=\frac{5}{4}+\frac{5}{8}+\frac{5}{16}+\frac{5}{32}+\frac{5}{64}\)
\(\Leftrightarrow E=\frac{5}{2^2}+\frac{5}{2^3}+\frac{5}{2^4}+\frac{5}{2^5}+\frac{5}{2^6}\)
\(\Leftrightarrow E=5\left(\frac{1}{2^2}+\frac{1}{2^3}+\frac{1}{2^4}+\frac{1}{2^5}+\frac{1}{2^6}\right)\)
Đặt \(A=\frac{1}{2^2}+\frac{1}{2^3}+\frac{1}{2^4}+\frac{1}{2^5}+\frac{1}{2^6}\)
\(\Rightarrow2A=\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+\frac{1}{2^4}+\frac{1}{2^5}\)
\(\Rightarrow2A-A=\left(\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+\frac{1}{2^4}+\frac{1}{2^5}\right)-\left(\frac{1}{2^2}+\frac{1}{2^3}+\frac{1}{2^4}+\frac{1}{2^5}+\frac{1}{2^6}\right)\)
\(\Rightarrow A=\frac{1}{2}-\frac{1}{2^6}\)
Thay \(A=\frac{1}{2}-\frac{1}{2^7}\)vào E ta được:
\(E=5\cdot\left(\frac{1}{2}-\frac{1}{2^6}\right)\)
6 tháng 7 2020
Bài làm
~ Đề là tính E, mà làm theo cách của bạn Vũ Hà My đây thì nó lại vừa dài, vừa khó ra kết quả. Nên mik sẽ làm theo cách quy đồng nhé. Dấu " . " là dấu nhân nha. ~
\(E=\frac{5}{4}+\frac{5}{8}+\frac{5}{16}+\frac{5}{32}+\frac{5}{64}\)
\(E=5.\left(\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}\right)\)
\(E=5.\left(\frac{16}{64}+\frac{8}{64}+\frac{4}{64}+\frac{2}{32}+\frac{1}{64}\right)\)
\(E=5.\frac{31}{64}\)
\(E=\frac{155}{64}\)
Vậy \(E=\frac{155}{64}\)
NN
1
28 tháng 6 2018
TRA LOI:
1+5/4+5/8+5/16+5/32+5/64=219/64
3+3/5+3/25+3/125+3/512=3,8
DQ
0
Đặt \(A=1+\frac{5}{4}+\frac{5}{8}+\frac{5}{16}+\frac{5}{32}+\frac{5}{64}\)
\(=5\cdot\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}\right)\)
Đặt \(B=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}\)
\(\Rightarrow2\cdot B=1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}\)
\(\Rightarrow B=2\cdot B-B=1-\frac{1}{64}=\frac{63}{64}\)
\(\Rightarrow A=5\cdot\frac{63}{64}=\frac{315}{64}\)