a. 1 + 2 + 4 + 8 + 16 +…+ 512
b. 1 + 3 + 9 + 27 + 81+… +729
6h mik đi học ùi giúp iii
Tính nhanh:
a) 2/9+6/27+8/36+12/54+16/72+18/81
b) ( 1-2/5) * ( 1-2/7 ) * ( 1-2/9 ) *.....................( 1-2/99)
c) Tính tổng sau bằng cách hợp lí và nhanh nhất
1/2+1/4+1/8+1/16+........................+1/1024
Giúp mik nha các bạn, mik đang cần lắm đó!
a)
Vì 2/9=6/27=8/36=12/54=16/72=18/81 nên:
2/9+6/27+8/36+12/54+16/72+18/81=
2/9+2/9+2/9+2/9+2/9+2/9=
2/9*6=
12/9=
4/3
Vậy 2/9+6/27+8/36+12/54+16/72+18/81=4/3
b)
Ta có:
1-2/5=3/5
1-2/7=5/7
1-2/9=7/9
...
1-2/99=97/99
Vậy (1-2/5)*(1-2/7)*(1-2/9)*...*(1-2/99)=
3/5*5/7*7/9*...*97/99=
(3*5*7*...*97)/(5*7*9*...*99)=
3/99=
1/33
Vậy (1-2/5)*(1-2/7)*(1-2/9)*...*(1-2/99)=1/33
c)
Gọi biểu thức 1/2+1/4+1/8+1/16+...+1/1024 là S,ta có:
S=1/2+1/4+1/8+1/16+...+1/1024
S*2=1+1/2+1/4+1/8+...+1/512
S*2-S=(1+1/2+1/4+1/8+...+1/512)-(1/2+1/4+1/8+1/16+...+1/1024)
S=1-1/1024
S=1023/1024
Vậy 1/2+1/4+1/8+1/16+...+1/1024=1023/1024
Tính
a) 9/8 - 8/9 = 8/25 + 1/4 - 5/16 + 19/25 - 1/9 + 2/25 - 1/81
b) -1/3 + 4/5 - 8/35 + -2/9 - 1/135 + -4/9 + 3/7
Các bn giải giúp mình nha chiều nay mk phải đi học rùi
Làm chi tiết nha
tính nhanh p/s 1+ 5/4 + 5/8 + 5/16 + 5/32 + 5/64
b) 1/3 +1/9 + 1/27 + 1/81 +...........+ 1/59049
c) 3/2 + 3/8 + 3/32 +3/128 + 3/512
d) 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + 1/128 + 1/256 giúp mình với
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
tính nhanh
a) 1/2+1/4+1/8+1/16+1/32
b) 1/3+1/9+1/27+1/81+1/243+1/729
A = \(\dfrac{1}{2}\) + \(\dfrac{1}{4}\) + \(\dfrac{1}{8}\) + \(\dfrac{1}{16}\) + \(\dfrac{1}{32}\)
2 \(\times\) A = 1 + \(\dfrac{1}{2}\) + \(\dfrac{1}{4}\) + \(\dfrac{1}{8}\) + \(\dfrac{1}{16}\)
2 \(\times\) A - A = 1 + \(\dfrac{1}{2}\) + \(\dfrac{1}{4}\) + \(\dfrac{1}{8}\) + \(\dfrac{1}{16}\) - (\(\dfrac{1}{2}\) + \(\dfrac{1}{4}\) + \(\dfrac{1}{8}\) + \(\dfrac{1}{16}\) + \(\dfrac{1}{32}\))
A = 1 + \(\dfrac{1}{2}\) + \(\dfrac{1}{4}\) + \(\dfrac{1}{8}\) + \(\dfrac{1}{16}\) - \(\dfrac{1}{2}\) - \(\dfrac{1}{4}\) - \(\dfrac{1}{8}\) - \(\dfrac{1}{16}\) - \(\dfrac{1}{32}\)
A = 1 - \(\dfrac{1}{32}\)
A = \(\dfrac{31}{32}\)
B = \(\dfrac{1}{3}\) + \(\dfrac{1}{9}\) + \(\dfrac{1}{27}\) + \(\dfrac{1}{81}\) + \(\dfrac{1}{243}\) + \(\dfrac{1}{729}\)
3 \(\times\)B = 1 + \(\dfrac{1}{3}\) + \(\dfrac{1}{9}\) + \(\dfrac{1}{27}\) + \(\dfrac{1}{81}\) + \(\dfrac{1}{243}\)
3 \(\times\) B - B = 1 + \(\dfrac{1}{3}\) + \(\dfrac{1}{9}\) + \(\dfrac{1}{27}\) + \(\dfrac{1}{81}\) + \(\dfrac{1}{243}\) -(\(\dfrac{1}{3}\)+\(\dfrac{1}{9}\)+\(\dfrac{1}{27}\)+...+\(\dfrac{1}{729}\))
2B = 1 + \(\dfrac{1}{3}\) + \(\dfrac{1}{9}\) + \(\dfrac{1}{27}\) + \(\dfrac{1}{81}\) + \(\dfrac{1}{243}\) - \(\dfrac{1}{3}\) - \(\dfrac{1}{9}\)-\(\dfrac{1}{27}\)-...- \(\dfrac{1}{729}\)
2B = 1 - \(\dfrac{1}{729}\)
2B = \(\dfrac{728}{729}\)
B = \(\dfrac{728}{729}\) : 2
B = \(\dfrac{364}{729}\)
S = \(81\) + \(27\) + \(9\) + \(3\) ... + \(\dfrac{1}{27}\) + \(\dfrac{1}{81}\)
Tính S giúp mik với ạ, ai nhanh mik tick
\(3S=241+81+27+9+...+\dfrac{1}{9}+\dfrac{1}{27}\)
\(2S=3S-S=241-\dfrac{1}{81}=\dfrac{241x81-1}{81}\)
\(\Rightarrow S=\dfrac{241x81-1}{2x81}\)
b.1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256
c.1/3+1/9+1/27+1/81+1/283+1/729
giúp mình
Tính 1 + 2 - 3 - 4 + 5 + 6 - 7 - 8 + 9 + .... 26 - 27 - 28 + 29 + 30 tính giùm mik nha thanks thứ 6 mik đi học rồi
\(=1+2+\left(5+6-3-4\right)+\left(9+10-7-8\right)+...+\left(29+30-27-28\right)\)
\(=1+2+4+4+...+4\)( có 7 số 4)
\(=3+7\times4=31\)
1 + 2 - 3 - 4 + 5 + 6 - 7 - 8 + 9 + .... 26 - 27 - 28 + 29 + 30
= 1+ 2 + ( 5 + 6 + -3 -4 ) + ( 9 + 10 - 7 - 8 ) + ... + ( 29 + 30 - 27 - 28 )
= 1 + 2 + 4 + 4 + ... + 4 ( có 7 chữ số 4 )
= 1+ 2 + 4 x 7
= 1 + 2 + 28 = 31
# Hok_tốt nha
Tính giá trị các biểu thức sau (Tính nhanh nếu có thể):
a, 32/12 - 18/27 - 17/4 + 5/3
b, -5/9 - 4/12 + 7/6 - 1/3
c,-7/18 - 11/16 + 1/3 - 7/8
giúp m v mn mai mình đi học r
Tính bằng cách thuận tiện:
a.A=1/2+1/4+1/8+1/16+1/32+1/64
b.B=1/3+1/9+1/27+1/81+1/243
\(A=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}\)
\(A=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{8}+\frac{1}{8}-\frac{1}{16}+\frac{1}{16}-\frac{1}{32}+\frac{1}{32}-\frac{1}{64}\)
\(A=1-\frac{1}{64}\)
\(A=\frac{63}{64}\)
\(B=\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}+\frac{1}{243}\)
\(3B=1+\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}\)
\(3B-B=1-\frac{1}{243}\)
\(2B=\frac{242}{243}\)
\(B=\frac{242}{243}\div2\)
\(B=\frac{121}{243}\)
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