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a.\(\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)...\left(1-\frac{1}{2015}\right)=\frac{1}{2}.\frac{2}{3}...\frac{2014}{2015}=\frac{1.2.3...2014}{2.3...2015}=\frac{1}{2015}\)
b.\(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...+\frac{1}{256}=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{8}+...+\frac{1}{128}-\frac{1}{256}=1-\frac{1}{256}=\frac{255}{256}\)
c.\(\frac{5}{2}+\frac{5}{4}+\frac{5}{8}+...+\frac{5}{256}=5\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...+\frac{1}{256}\right)=5.\frac{255}{256}=\frac{1275}{256}\)
d.14,35+(13,7-13,6).1=14,35+0,1.1=14,35+0,1=14,45
\(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+....+\frac{1}{256}=\left(1-\frac{1}{2}\right)+\left(\frac{1}{2}-\frac{1}{4}\right)+\left(\frac{1}{4}-\frac{1}{8}\right)+...+\left(\frac{1}{128}-\frac{1}{256}\right)\)
\(=1-\frac{1}{256}=\frac{255}{256}\)
1/2+1/4+1/8+……+1/256
=(1-1/2)+(1/2-1/4)+(1/4-1/8)+......+(1/128-1/256)
=1-1/2+1/2-1/4+1/4-1/8+......+1/128-1/256
=1-1/256
=255/256
a, 1+2+4+8+16+32+...+256+512+1024
= 20+21+22+23+24+25+...+28+29+210
= 1 + 2 + 22+3+4+5+...+8+9+10
= 3+254
mink lm đc câu D thôi
D=1/2+1/4+1/8+...+1/256
D=1-1/2+1/2-1/4+1/4-1/8+1/8-1/16+....+1/128-1/256
D=1-1/256
D=255/256