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1/2+1/4+1/8+1/16+1/32
=1-1/2+1/2-1/4+1/4-1/8+1/8-1/16+1/16-1/32
=1-1/32
=31/32
\(A=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}\)
\(A=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{8}+\frac{1}{8}-\frac{1}{16}+\frac{1}{16}-\frac{1}{32}+\frac{1}{32}-\frac{1}{64}\)
\(A=1-\frac{1}{64}\)
\(A=\frac{63}{64}\)
\(B=\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}+\frac{1}{243}\)
\(3B=1+\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}\)
\(3B-B=1-\frac{1}{243}\)
\(2B=\frac{242}{243}\)
\(B=\frac{242}{243}\div2\)
\(B=\frac{121}{243}\)
a.A=1/2+1/4+1/8+1/16+1/32+1/64
A= \(\frac{1}{1\cdot2}+\frac{1}{2\cdot2}+\frac{1}{2\cdot4}+\frac{1}{4\cdot4}+\frac{1}{4\cdot8}+\frac{1}{8\cdot8}\)
= \(\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{2}+\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{4}+\frac{1}{4}-\frac{1}{8}+\frac{1}{8}-\frac{1}{8}\)
= 1 - 1/8 = 7/8
b.B=1/3+1/9+1/27+1/81+1/243
B= \(\frac{1}{1\cdot3}+\frac{1}{3\cdot3}+\frac{1}{3\cdot9}+\frac{1}{9\cdot9}+\frac{1}{9\cdot27}\)
= 1 - 1/27 = 26/27
\(\dfrac{1}{4}:0,25-\dfrac{1}{8}:0,125+\dfrac{1}{2}:0,5-\dfrac{1}{16}:0,0625\\ =0,25:0,25-0,125:0,125+0,5:0,5-0,0625:0,0625\\ =1-1+1-1\\ =0+1-1\\ =1-1\\ =0\)
\(ĐặtA=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}\)
\(2A=1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}\)
\(2A-A=\left(1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}\right)-\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}\right)\)
\(A=1-\frac{1}{64}=\frac{63}{64}\)
Trả lời:
1/3+1/2+1/5+12/15+22/33+16/32=
(1/3+22/33)+(1/5+12/15)+(1/2+16/32)
=1+1+1=3
\(\dfrac{1}{4}\) : 0,25 - \(\dfrac{1}{8}\) : 0,125 + \(\dfrac{1}{2}\) : 0,5 - 1
= 0,25 x 4 - 0,125 x 8 + 0,5 x 2 - 1
= 1 - 1 + 1 - 1
= 0 + 1 - 1
= 1 - 1
= 0
A = \(\dfrac{1}{4}\) : 0,25 - \(\dfrac{1}{8}\): 0,125 + \(\dfrac{1}{2}\): 0,5 - 1
A = \(\dfrac{1}{4}\) x 4 - \(\dfrac{1}{8}\) x 8 + \(\dfrac{1}{2}\) x 2 - 1
A = 1 - 1 + 1 - 1
A = (1 - 1) + (1 - 1)
A = 0
\(\dfrac{1}{10}+\dfrac{1}{2}:0,5-\dfrac{1}{4}:0,25+\dfrac{1}{8}:0,125\)
\(=\dfrac{1}{10}+\dfrac{1}{2}\times2-\dfrac{1}{4}\times4+\dfrac{1}{8}\times8\)
\(=\dfrac{1}{10}+1-1+1\)
\(=\dfrac{1}{10}+1=\dfrac{1}{10}+\dfrac{10}{10}=\dfrac{11}{10}\)
đặt A=\(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}\)
A=\(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{8}+\frac{1}{8}-\frac{1}{16}+\frac{1}{16}-\frac{1}{32}\)
A=\(1-\frac{1}{32}\)
A=\(\frac{31}{32}\)
1/2 + 1/4 + 1/8 + 1/16 + 1/32
= ( 1/2 + 1/4 ) + ( 1/8 + 1/16 ) + 1/32
= 3/4 + 3/16 + 1/32
= 3/4 + ( 3/16 + 1/32 )
= 3/4 + 7/32
=31/32