a)1 /2+ 1/4+1/8+1/16+1/32+...+1/256 giúp mk vs mk cần gấp nha😉
Tính (16*8-1)/(2+1)(2*2+1)(2*4+1)(2*8+1)(2*16+1)
Giúp mk vs 😉😉
dưới mẫu nè: (2+1)(2^2+1)(2*4+1)(2*8+1)(2*16+1)=(2*4-1)(2*4+1)(2*8+1)(2*16+1)(*vì 2+1=2*2-1)
cứ như thế thì được: 2*32-1
Ta có : \(\frac{16^8-1}{\left(2+1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)}\)
\(=\frac{\left(2^4\right)^8-1}{\left(2-1\right)\left(2+1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)}\)
\(=\frac{2^{32}-1}{\left(2^2-1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)}\)
\(=\frac{2^{32}-1}{\left(2^4-1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)}\)
\(=\frac{2^{32}-1}{\left(2^8-1\right)\left(2^8+1\right)\left(2^{16}+1\right)}\)
\(=\frac{2^{32}-1}{\left(2^{16}-1\right)\left(2^{16}+1\right)}\)
\(=\frac{2^{32}-1}{2^{32}-1}=1\)
Tìm x, biêt:
(1/8+1/16+1/32+1/64+1/128+1/256)*x=1/512
giúp mk nha
Đặt \(A=\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}+\frac{1}{128}+\frac{1}{256}\)
\(A=\frac{1}{2^3}+\frac{1}{2^4}+\frac{1}{2^5}+\frac{1}{2^6}+\frac{1}{2^7}+\frac{1}{2^8}\)
\(2A=\frac{1}{2^2}+\frac{1}{2^3}+\frac{1}{2^4}+\frac{1}{2^5}+\frac{1}{2^6}+\frac{1}{2^7}\)
\(2A-A=\left(\frac{1}{2^2}+\frac{1}{2^3}+\frac{1}{2^4}+\frac{1}{2^5}+\frac{1}{2^6}+\frac{1}{2^7}\right)-\left(\frac{1}{2^3}+\frac{1}{2^4}+\frac{1}{2^5}+\frac{1}{2^6}+\frac{1}{2^7}+\frac{1}{2^8}\right)\)
\(A=\frac{1}{2^2}-\frac{1}{2^8}\)
\(A=\frac{1}{4}-\frac{1}{256}=\frac{63}{256}\)
\(\Rightarrow\frac{63}{256}.x=\frac{1}{512}=\frac{1}{2^9}\)
\(\Rightarrow\frac{63}{2^8}.x=\frac{1}{2^9}\)
\(\Rightarrow x=\frac{1}{2^9}:\frac{63}{2^8}=\frac{1}{2^9}.\frac{2^8}{63}=\frac{1}{2.63}=\frac{1}{126}\)
Ủng hộ mk nha !!! ^_^
Giúp mk câu này
1/2+1/4+1/6+1/8+1/16+.......+1/128+1/256
Giúp mk nha
Đặt : \(A=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+.....+\frac{1}{128}+\frac{1}{256}\)
\(\Rightarrow2A=1+\frac{1}{2}+\frac{1}{4}+.....+\frac{1}{128}\)
\(\Rightarrow2A-A=1-\frac{1}{256}\)
\(\Rightarrow A=\frac{255}{256}\)
Bài 1: Tính tổng sau:
a) 5/2 + 5/6 + 5/18 + 5/54 + 5/162
b) 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + 1/128 + 1/256
giải giúp mk và kb nha!!!!!!!!!!!!!
B)A*2=(1/2+1/4+....+1/256)*2
=1+1/2+1/4+....+1/128)
A*2-A=(1+1/2+1/4+...+1/128)-(1/2+1/4+...+1/256)
=1-1/256
=255/256
a) Đặt A = \(\frac{5}{2}+\frac{5}{6}+\frac{5}{18}+\frac{5}{54}+\frac{5}{162}\)
\(\Rightarrow\frac{1}{3}\times A=\frac{5}{6}+\frac{5}{18}+\frac{5}{54}+\frac{5}{162}+\frac{5}{486}\)
Lấy \(A-\frac{1}{3}\times A\)theo vế ta có :
\(A-\frac{1}{3}\times A=\left(\frac{5}{2}+\frac{5}{6}+\frac{5}{18}+\frac{5}{54}+\frac{5}{162}\right)-\left(\frac{5}{6}+\frac{5}{18}+\frac{5}{54}+\frac{5}{162}+\frac{5}{486}\right)\)
\(\Rightarrow\frac{2}{3}\times A=\frac{5}{2}-\frac{5}{486}\)
\(\Rightarrow\frac{2}{3}\times A=\frac{605}{243}\)
\(\Rightarrow A=\frac{605}{243}:\frac{2}{3}\)
\(\Rightarrow A=\frac{605}{162}\)
Vậy \(\frac{5}{2}+\frac{5}{6}+\frac{5}{18}+\frac{5}{54}+\frac{5}{162}=\frac{605}{162}\)
b) Đặt B = \(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...+\frac{1}{128}+\frac{1}{256}\)
=> \(\frac{1}{2}\times B=\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+...+\frac{1}{256}+\frac{1}{512}\)
Lấy B trừ \(\frac{1}{2}\times B\)theo vế ta có :
\(B-\frac{1}{2}\times B=\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{6}+...++\frac{1}{128}+\frac{1}{256}\right)-\left(\frac{1}{4}+\frac{1}{6}+\frac{1}{8}+...+\frac{1}{512}\right)\)
\(\Rightarrow\frac{1}{2}\times B=\frac{1}{2}-\frac{1}{512}\)
\(\Rightarrow\frac{1}{2}\times B=\frac{255}{512}\)
\(\Rightarrow B=\frac{255}{512}:\frac{1}{2}\)
\(\Rightarrow B=\frac{255}{256}\)
Vậy \(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+...+\frac{1}{256}=\frac{255}{256}\)
a ) 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + 1/128 + 1/256
b) 1/3 + 1/9 + 1/27 + 1/81 + 1/243 + 1/29
Các bn giúp mk nha ! À lưu ý : Dấu / nghĩa là dấu gạch của phân số nha .
a ) 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + 1/128 + 1/256
Đạt A = 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + 1/128 + 1/256
A x 2 = 2 x ( 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + 1/128 + 1/256)
A x 2 = 1 + 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + 1/128
Lấy A x 2 - A ta có :
A x 2 - A = 1 + 1/2 + ..... + 1/128 - 1/2 + 1/4 + ........ + 1/256
A x ( 2 - 1 ) = 1 - 1/ 256
A = 255/256
b) 1/3 + 1/9 + 1/27 + 1/81 + 1/243 + 1/729
Đặt A = 1/3 + 1/9 + 1/27 + 1/81 + 1/243 + 1/729
A x 3 = 3 x ( 1/3 + 1/9 + 1/27 + 1/81 + 1/243 + 1/729)
= 1 + 1/ 3 + 1/9 + 1/27 + 1/81 + 1/243
Lấy A x 3 - A ta có :
A x 3 - A = 1 + 1/3 + 1/9 +..... + 1/243 - 1/3 + 1/9 +........+ 1/243 + 1/29
A x ( 3 - 1 ) = 1 - 1/29
A x2 = 28/29
A = 28/29 : 2 ( tự tính
Đặt A = \(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+.....+\frac{1}{256}\)
\(\Rightarrow2A=1+\frac{1}{2}+\frac{1}{4}+.....+\frac{1}{128}\)
\(\Rightarrow2A-A=1-\frac{1}{256}\)
\(\Rightarrow A=\frac{255}{256}\)
rút gọn biểu thức
a) A=16^8 -1/(2+1)(2^2+1)(2^4+1)(2^8+1(3^16+1)
b) B=(3+1)(3^2+1)(3^4+1)(3^8+1)(3^16+1)/9^16-1
giúp mk vs ah mk đang cần gấp ah
a) Ta có: \(A=\dfrac{16^8-1}{\left(2+1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)}\)
\(=\dfrac{2^{32}-1}{\left(2^2-1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)}\)
\(=\dfrac{2^{32}-1}{\left(2^4-1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)}\)
\(=\dfrac{2^{32}-1}{\left(2^8-1\right)\left(2^8+1\right)\left(2^{16}+1\right)}\)
\(=\dfrac{2^{32}-1}{\left(2^{16}-1\right)\left(2^{16}+1\right)}\)
\(=\dfrac{2^{32}-1}{2^{32}-1}=1\)
b) Ta có: \(B=\dfrac{\left(3+1\right)\left(3^2+1\right)\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)}{9^{16}-1}\)
\(=\dfrac{\left(3^2-1\right)\cdot\left(3^2+1\right)\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)}{2\cdot\left(3^{32}-1\right)}\)
\(=\dfrac{\left(3^4-1\right)\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)}{2\cdot\left(3^{32}-1\right)}\)
\(=\dfrac{\left(3^8-1\right)\left(3^8+1\right)\left(3^{16}+1\right)}{2\left(3^{32}-1\right)}\)
\(=\dfrac{\left(3^{16}-1\right)\left(3^{16}+1\right)}{2\left(3^{32}-1\right)}=\dfrac{1}{2}\)
Các bạn giúp mk vs ak mk đag cần gấp lắm
Rút gọn biểu thức : a) (3+1)(3^2+1)(3^4+1)(3^8+1)(3^16+1)(3^32+1)
b) 2x(2x-1)^2 - 3x(x+3)(x-3) - 4x(x+1)^2
A=1+4+16+64+256+1024 tính nhanh tổng mk cần gấp lắm nha
=(1+4)+(16+1024)+(64+256)
=5+1040+320
=5+1360
=1365
k mun suy nghi nhiu thi lam nhu z
tính nhanh 1/4+1/8+1/16+1/32+1/64+1/128+1/256+1/512
AI GIÚP MÌNH SẼ CHO MỘT MK
#)Giải :
\(\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}+\frac{1}{128}+\frac{1}{256}+\frac{1}{512}\)
\(=\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{8}+\frac{1}{8}-\frac{1}{16}+...+\frac{1}{256}-\frac{1}{512}\)
\(=\frac{1}{2}-\frac{1}{512}\)
\(=\frac{255}{512}\)
Lời giải
\(=\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{8}+\frac{1}{8}-\frac{1}{16}+...+\frac{1}{256}-\frac{1}{512}\)
\(=\frac{1}{2}-\frac{1}{512}\)
\(=\frac{255}{512}\)