a)1/2+1/6+1/12+........+1/9900+1/10100
b)1/2+1/4+1/8+....+1/256+1/512
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BT
1
26 tháng 6 2015
a) trieu dang làm rồi
b) A= 1/2 + 1/4+ 1/8+ 1/16 + 1/32 + 1/64 + 1/128 + 1/256 + 1/512
A = 1 - 1/2 + 1/2- 1/4 + 1/4 - 1/8 + 1/8 - 1/16 + 1/16 - 1/32 + 1/32 - 1/64 + 1/64 - 1/128 + 1/128 - 1/256 - 1/256 - 1/512
A = 1 - 1/512
A = 511/512
26 tháng 8 2016
\(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}\)
\(=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}\)
\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}\)
\(=1-\frac{1}{5}\)
\(=\frac{4}{5}\)
\(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{9900}\)
\(=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{98.99}+\frac{1}{99.100}\)
\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+....+\frac{1}{98}-\frac{1}{99}+\frac{1}{99}-\frac{1}{100}+\frac{1}{100}\)
\(=1-\frac{1}{100}\)
\(=\frac{99}{100}\)
29 tháng 4 2015
Đặt A=1/2+1/4+1/6+1/8+1/16+...+1/256+1/512
=(1/2+1/4+1/8+1/16+...+1/256+1/256-1/512)+1/6
=(1-1/2+1/2-1/4+1/4-1/8+1/8-1/16+...+1/128-1/256+1/256-1/512)+1/6
=1-1/512+1/6
=1789/1536
Vậy A=1789/1536
3 tháng 10 2021
\(A=\dfrac{1}{2}+\dfrac{1}{2^2}+\dfrac{1}{2^3}+...+\dfrac{1}{2^9}\\ 2A=1+\dfrac{1}{2}+\dfrac{1}{2^2}+...+\dfrac{1}{2^8}\\ 2A-A=\left(1+\dfrac{1}{2}+...+\dfrac{1}{2^8}\right)-\left(\dfrac{1}{2}+\dfrac{1}{2^2}+...+\dfrac{1}{2^9}\right)\\ A=1-\dfrac{1}{2^9}=\dfrac{511}{512}\)
7 tháng 7 2016
A=1/2+1/4+1/8.....+1/256+1/512
2A=1+1/2+1/4+1/8...1/256
A=(1+1/2+1/4+1/8...1/256)-(1/2+1/4+1/8.....+1/256+1/512)
A=1-1/512
A=511/512
511/512
VD
1
PV
19 tháng 4 2016
Ta có: A =1/2+1/4+1/8+1/16+....+1/256+1/512
=> 2A = 1 + 1/2 + 1/4 + 1/8 + ...+ 1/128 + 1/256
=> 2A - A = (1 + 1/2 + 1/4 + 1/8 + ...+ 1/128 + 1/256 -(1/2+1/4+1/8+1/16+....+1/256+1/512 )
A = 1 - 1/512 = 511/512
LT
2
8 tháng 6 2019
1/2 + 1/4+ 1/8+ 1/16 + 1/32 + 1/64 + 1/128 + 1/256 + 1/512
= 1 – 1/2 + 1/2- 1/4 + 1/4 – 1/8 + 1/8 – 1/16 + 1/16 – 1/32 + 1/32 – 1/64 + 1/64 – 1/128 + 1/128 – 1/256 – 1/256 – 1/512
= 1 – 1/512
= 511/512
hok tot
a, \(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+....+\frac{1}{10100}\)
=\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+....+\frac{1}{100.101}\)
=\(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+......+\frac{1}{100}-\frac{1}{101}\)
=\(1-\frac{1}{101}\)
=\(\frac{100}{101}\)
b,\(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+....+\frac{1}{512}\)
=\(\left(1-\frac{1}{2}\right)+\left(\frac{1}{2}-\frac{1}{4}\right)+\left(\frac{1}{4}-\frac{1}{8}\right)+...+\left(\frac{1}{256}-\frac{1}{512}\right)\)
=\(1-\frac{1}{512}\)
=\(\frac{511}{512}\)
\(\frac{1}{2}+\frac{1}{6}+...+\frac{1}{9900}+\frac{1}{10100}\)
\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{99}-\frac{1}{100}+\frac{1}{100}-\frac{1}{101}\)
\(=1-\frac{1}{101}=\frac{100}{101}\)