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tong tren co 10 so hang suy ra ps cuoi cung la 1/2014
Suy ra tong=1023/1024
2A=\(2x\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}+\frac{1}{128}+\frac{1}{256}+\frac{1}{512}+\frac{1}{1024}\right)\)
2A=\(1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}+\frac{1}{128}+\frac{1}{256}+\frac{1}{512}\)
2A-A=\(1-\frac{1}{1024}\)
A=\(\frac{1023}{1024}\)
1/4+1/8+1/16+...
=1/4+1/8+1/16+1/32+1/64+1/128+1/256+1/512+1/1024+1/2048
=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+1/512-1/1024+1/1024-1/2048
=1/2-1/2048
=1024/2048-1/2048
=1023/2048
A=1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256+1/512+1/1024
A=1/1*2+1/4*2+1/8*2+1/16*2+1/32*2+1/64*2+1/128*2+1/256*2+1/512*2
A*2=1+(1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256+1/512)-1/1024
A*2-A=511/512+1/1024
A=1023/1024
2a=\(1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}+\frac{1}{128}+\frac{1}{256}+\frac{1}{512}\)
2a-a=\(1-\frac{1}{1024}\)
a=\(1-\frac{1}{1024}\)
a=\(\frac{1023}{1024}\)
a = 1/2+1/4+1/8+1/16
= (1 - 1/2) + (1/2 -1/4) + (1/4 - 1/8) + ... + (1/512 - 1/1024).
= 1 - 1/1024
= 1023/1024
A=1/2+1/4+1/8+1/16
A=1/2+(1/2-1/4)+(1/4-1/8)+(1/8-1/16)+....+(1/512-1/1024)
=1/2+1/2-1/1024
=1-1/1024=1023/1024
DS : 1023/1024