a: 4A=4+4^2+...+4^9

=>3A=4^9-1

=>A=(4^9-1)/3

b: 2A=1+1/2+...+1/2^7

=>A=1-1/256=255/256

c: =1-1/5+1/5-1/9+...+1/85-1/89

=1-1/89=88/89

d: =1/3(3/1*4+3/4*7+...+3/304*307)

=1/3(1-1/4+1/4-1/7+...+1/304-1/307)

=1/3*306/307=102/307

e: E=1-1/2+1/2-1/3+...+1/11-1/12

=1-1/12=11/12

g: =2/5(1-1/6+1/6-1/11+...+1/96-1/101)

=2/5*100/101=40/101

???

b= 1/4 +1/16+1/64+1/256+...+1/16384

4b = 1+ 1/4 +1/16 + 1/64+... +1/4096

4b-b = 1 -1/16384

3b = 16383/16384

b = 49149/16384

\(A=\frac{1}{4}+\frac{1}{16}+\frac{1}{64}+...+\frac{1}{16384}\)

\(A=\frac{1}{2^2}+\frac{1}{2^4}+...+\frac{1}{2^{14}}\)

\(2^2A=1+\frac{1}{2^2}+...+\frac{1}{2^{12}}\)

\(4A-A=\left(1+\frac{1}{2^2}+...+\frac{1}{2^{12}}\right)-\left(\frac{1}{2^2}+\frac{1}{2^4}+...+\frac{1}{2^{14}}\right)\)

\(3A=1-\frac{1}{2^{14}}\)

\(A=\frac{1-\frac{1}{2^{14}}}{3}\)

mình cũng đang phân vân câu này

ahihi đồ ngốc,thật sự thì mình không biết nữa...

B = \(\frac{1}{2}+\frac{1}{3}+\frac{1}{6}+\frac{1}{12}+\frac{1}{15}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{63}\)

B = \(\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{6}\right)+\left(\frac{1}{12}+\frac{1}{15}+\frac{1}{20}\right)+\left(\frac{1}{30}+\frac{1}{42}+\frac{1}{56}\right)+\frac{1}{63}\)

B = \(1+\frac{1}{5}+\frac{3}{40}+\frac{1}{63}\)

B = \(1\frac{11}{40}+\frac{1}{63}\)

B = \(1\frac{733}{2520}\)

nguyentuantai làm hòa với Nguyễn Đình Dũng phải chăng mục đích là lấy **** ko

a) 1 + 1/4 + 1/8 + 1/16

= 16/16 + 4/16 + 2/16 + 1/16

= 23/16

b) 2 - 1/8 - 1/12 - 1/16

= 96/48 - 6/46 - 4/48 - 3/48

= 83/48

c) 4/99 × 18/5 : 12/11 + 3/5

= 8/55 : 12/11 + 3/5

= 2/15 + 3/5

= 2/15 + 9/15

= 11/15

d) (1 - 3/4) × (1 + 1/3) : (1 - 1/3)

= 1/4 × 4/3 : 2/3

= 1/3 : 2/3

= 2

1 + 1/4 + 1/8 + 1/16

= 16 + 4 + 2 + 1 / 16

=23/16

2-1/8-1/12-1/16

= 96 - 6 - 4 - 3 / 48

= 83 / 48

4/99 x 18/5 : 12 /11 + 3/5

= 4/99 x 18/5 x 11/12 + 3/5

= 2/15 + 3/5

= 11/15

(1 - 3/4) x (1+1/3) : (1-1/3) 

= 1/4 x 4/3 : 2/3

= 1/4 x 4/3 x 3/2

= 1/2

\(16+64+256+1024+...+16384+65536\)

\(=4^2+4^3+4^4+....+4^7+4^8\)

Đặt : \(A=4^2+4^3+4^4+....+4^7+4^8\)

\(\Rightarrow4A=4^3+4^4+4^5+...+4^8+4^9\)

\(\Rightarrow4A-A=\left(4^3+4^4+4^5+...+4^8+4^9\right)-\left(4^2+4^3+4^4+...+4^7+4^8\right)\)

\(\Rightarrow3A=4^9-4^2\)

\(\Rightarrow A=\frac{4^9-4^2}{3}=87376\)

Vậy : \(16+64+256+1024+...+16384+65536=87376\)

Bài làm

\(\frac{\left(1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}\right)}{\left(1-\frac{1}{2}+\frac{1}{4}-\frac{1}{8}+\frac{1}{16}\right)}\)

\(=\frac{\left(\frac{2}{2}+\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+\frac{1}{2^4}\right)}{\left(\frac{2}{2}-\frac{1}{2}+\frac{1}{2^2}-\frac{1}{2^3}+\frac{1}{2^4}\right)}\)

\(=\frac{\frac{1}{2}\left(2+1+\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}\right)}{\frac{1}{2}\left(2-1+\frac{1}{2}-\frac{1}{2^2}+\frac{1}{2^3}\right)}\)

\(=\frac{3+\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}}{1+\frac{1}{2}-\frac{1}{2^2}+\frac{1}{2^3}}\)

\(=\frac{\frac{24}{8}+\frac{4}{8}+\frac{2}{8}+\frac{1}{8}}{\frac{8}{8}+\frac{4}{8}-\frac{2}{8}+\frac{1}{8}}\)

\(=\frac{31}{8}\div\frac{11}{8}\)

\(=\frac{31}{8}\cdot\frac{8}{11}\)

\(=\frac{31}{11}\)

P/S: Trông không thuận tiện lắm :/

Hawy tính giúp mình nha mình cho đúng