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
a; 2^x . 16 = 128
b; 3^x : 9 = 27
c; ( 2 . x + 1) ^3 =27
d; ( x . 2 )^2= ( x . 2)^4
e; 2^x . 4 = 128
f; 85^x . 17^x= 625
g; ( x - 2)^4 = 4096
h; 3^x-1+5 . 3^x-1 = 162
a,2^x*16=128
2^x=8
2^x=2^3
suy ra x=3
b,3^x/9=27
3^x/3^2=3^3
3^x=3^5
suy ra x=5
c,(2*x+1)^3=27
(2*x+1)^3=3^3
suy ra 2*x+1=3
suy ra 2x=2
suy ra x=1
d,(x*2)^2=(x*2)^4
suy ra (x*2)^4-(x*2)^2=0
(x*2)^2*((x*2)^2-1)=0
suy ra (x*2)^2=0 hoac (x*2)^2-1=0
+(x*2)^2=0 +(x*2)^2-1=0
suy ra x*2=0 (x*2)^2=1
suy ra x=0 suy ra x*2=1 hoac -1
suy ra x=1/2 hoac -1/2
e,2^x*4=128
2^x=32
2^x=2^5
suy ra x=5
f,85^x*17^x=625
1445^x=625(vo ngiem)
g,(x-2)^4=4096
(x-2)^4=8^4
suy ra x-2=8
suy ra x=10
h,3^(x-1)+5*3*(x-1)=162
6*3^(x-1)=162
3^(x-1)=27
3^(x-1)=3^3
suy ra x-1=3
suy ra x=4
So sánh :
a) A = 2^16 và B = (2+1).(2^2+1).(2^4+1).(2^8+1)
b) A = 4.(3^2+1).(3^4+1)....(3^64+1) và B = 3^128-1
Câu a : Ta có :
\(B=\left(2+1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\)
\(=\left(2^2-1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\)
\(=\left(2^4-1\right)\left(2^4+1\right)\left(2^8+1\right)\)
\(=\left(2^8-1\right)\left(2^8+1\right)\)
\(=2^{16}-1< 2^{16}\)
Vậy \(A>B\)
Câu b : Ta có :
\(A=4\left(3^2+1\right)\left(3^4+1\right)...\left(3^{64}+1\right)\)
\(=\dfrac{8\left(3^2+1\right)\left(3^4+1\right)...\left(3^{64}+1\right)}{2}\)
\(=\dfrac{\left(3^2-1\right)\left(3^2+1\right)\left(3^4+1\right)...\left(3^{64}+1\right)}{2}\)
\(=\dfrac{\left(3^4-1\right)\left(3^4+1\right)...\left(3^{64}+1\right)}{2}\)
\(=\dfrac{...\left(3^{64}-1\right)\left(3^{64}+1\right)}{2}\)
\(=\dfrac{3^{128}-1}{2}< 3^{128}-1\)
Vậy \(A< B\)
tính nhanh
A = 1/1+2 +1/1+2+3 +1/1+2+3+4+...+...+...+1/1+2+3+4+...+2009
A = 1+1/2+1/4+1/8+...+1/4096+1/8192
BÀI TÍNH NHANH
A.2/3+2/6+2/12+2/24+2/48+2/96+2/192
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+1/243+1/729
D.3/2+3/8+3/32+3/128+3/512
E.3+3/5+3/25+3/125+3/625
a) = \(\frac{127}{96}\)
b) = \(\frac{255}{256}\)
c) Mik bỏ nha
d) = \(\frac{1023}{512}\)
e) = \(\frac{2343}{625}\)
Tính S = 1+1/2+1/4+1/8+1/16+........+1/2048+1/4096
Ta co: 2S=2+1+1/2+1/4+...+1/2048
2S-S=2+1+1/2+1/4+...+1/2048-1-1/2-1/4-...-1/2048-1/4096
\(\Rightarrow\)S=2-1/4096 =8191/4096
1) Tính nhanh: a)2/3+2/6+2/12+2/24+....+2/192
b)1/2+1/4+1/8+...+1/128
c)1/3+1/9+1/27+....+1/729
d)3/2+3/8+3/32+....+3/512
e)1/5+1/10+1/20+...+1/1280
Giai nhanh trong ngay hom nay nha cac ban
lam ho 1)A) 1- (5va4/9 +X -7va 7/18): 15va3/4=0
; B)X +1/2+1/4+1/8+1/16+1/32+1/64+1/128
---------------------------------------------------------- =9/2
1/3*4+1/4*5+1/5*6+1/6*7+1/7*8+1/8*9
2)
a)A=
5+8/17 +8/37
------------------
4+4/17+4/37
B)B=7/12+7/6+7/12+...+7/9900
Chưng tỏ
a, S= 1/2^2+1/3^2+...+1/9^2
Chứng tỏ 2/5<S<8/9
b, 1/2-1/4+1/8-1/16+1/32-1/64<1/3
c, 1/3-2/3^2+3/3^3-4/3^4+...+99/3^99-100/3^100<3/16
