a) A= 1/2 + 1/4+ 1/8+ 1/16 + 1/32 + 1/64 + 1/128 + 1/256 + 1/512 
A = 1 - 1/2 + 1/2- 1/4 + 1/4 - 1/8 + 1/8 - 1/16 + 1/16 - 1/32 + 1/32 - 1/64 + 1/64 - 1/128 + 1/128 - 1/256 - 1/256 - 1/512 
A = 1 - 1/512 
A = 511/512 

b) B = 1/3 + 1/9 + 1/27 + 1/81 + 1/243 + 1/729 
3B = 1 + 1/3 + 1/9 + 1/27 + 1/81 + 1/243 
3B - B = 1 - 1/729 
2B = 728/729 
B = 364/729

a) A= 1/2 + 1/4+ 1/8+ 1/16 + 1/32 + 1/64 + 1/128 + 1/256 + 1/512 
A = 1 - 1/2 + 1/2- 1/4 + 1/4 - 1/8 + 1/8 - 1/16 + 1/16 - 1/32 + 1/32 - 1/64 + 1/64 - 1/128 + 1/128 - 1/256 - 1/256 - 1/512 
A = 1 - 1/512 
A = 511/512 

b) B = 1/3 + 1/9 + 1/27 + 1/81 + 1/243 + 1/729 
3B = 1 + 1/3 + 1/9 + 1/27 + 1/81 + 1/243 
3B - B = 1 - 1/729 
2B = 728/729 
B = 364/729 

gọi A là biểu thức trên

ta có : A = 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + 1/128 + 1/256

      2A = 2. ( 1/2 + 1/4 + ... + 1/256 )

      2A = 1 + 1/2 + 1/4 + 1/8 + 1/16 +1/32 + 1/64 + 1/128

      2A - A = ( 1 + 1/2 + 1/4 + 1/8 + 1/16 +1/32 + 1/64 + 1/128) - ( 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + 1/128 + 1/256 )

   A = 1 - 1/256

   A  = 255/256

bài 1 tính nhanh

mik xin sửa đề câu a thành thế này ~

\(a,\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}+\frac{1}{128}+\frac{1}{256}\)

đặt \(A=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}+\frac{1}{128}+\frac{1}{256}\)

 \(A\cdot2=1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}+\frac{1}{128}\) 

\(A\cdot2-A=\) (  \(1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}+\frac{1}{128}\) )  - (  \(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}+\frac{1}{128}+\frac{1}{256}\) )

\(A=1-\frac{1}{256}\)

\(A=\frac{255}{256}\)

\(b,\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}+\frac{1}{243}+\frac{1}{729}\)

đặt \(B=\) \(\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}+\frac{1}{243}+\frac{1}{729}\) 

     \(B\cdot3=1+\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}+\frac{1}{243}\)

\(B\cdot3-B=\)  ( \(1+\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}+\frac{1}{243}\)) - \(\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}+\frac{1}{243}+\frac{1}{729}\) ) 

\(B\cdot2=\) \(1-\frac{1}{729}\)

\(B\cdot2=\frac{728}{729}\)

\(B=\frac{728}{729}:2\)

\(B=\frac{364}{729}\) 

\(c,\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}\)

ĐẶT \(C=\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}\)

    \(C=\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+\frac{1}{5\cdot6}\)

\(C=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}\)

\(C=\frac{1}{1}-\frac{1}{6}\)

\(C=\frac{5}{6}\)

Cảm ơn bạn nhé

\(A=\frac{1}{2}+\frac{1}{4}+...+\frac{1}{2048}\)

\(A=\left(1-\frac{1}{2}\right)+\left(\frac{1}{2}-\frac{1}{4}\right)+...+\left(\frac{1}{1024}-\frac{1}{2048}\right)\)

\(A=1-\frac{1}{2048}\)

\(\Rightarrow\)\(A=\frac{2047}{2048}\)

\(3B=1+\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}+\frac{1}{243}+\frac{1}{729}\)

\(3B-B=1-\frac{1}{2187}\)

\(2B=\frac{2186}{2187}\)

\(\Rightarrow B=\frac{2186}{4374}=\frac{1093}{2187}\)

a) = \(\frac{127}{96}\)

b) = \(\frac{255}{256}\)

c) Mik bỏ nha

d) = \(\frac{1023}{512}\)

e) = \(\frac{2343}{625}\)

bạn có thể trả lời rõ ra được ko

\(3A=3\cdot\left(\dfrac{1}{3}+\dfrac{1}{9}+\dfrac{1}{27}+\dfrac{1}{81}+\dfrac{1}{243}+\dfrac{1}{729}\right)\)

\(\Rightarrow3A=1+\dfrac{1}{3}+\dfrac{1}{9}+\dfrac{1}{27}+\dfrac{1}{81}+\dfrac{1}{243}\)

Lấy \(3A-A=1-\dfrac{1}{729}\)

\(\Rightarrow2A=\dfrac{728}{729}\Rightarrow A=\dfrac{364}{729}\)

A=1/3+1/9+1/27+1/81+1/243+1/729

3A=1+1/3+1/9+1/27+1/81+1/243

3A-A=(1+1/3+1/9+1/27+1/81+1/243)-(1/3+1/9+1/27+1/81+1/243+1/729)

3A-A=1-1/3+1/3-1/9+1/9-1/27+1/27-1/81+1/81-1/243+1/243-1/729)

2A=1-1/729

2A=728/729

A=728/729/2

A=364/729

Bài 1:

Bài 1: 1/3+1/9+1/27+1/81+1/243+1/729

Đặt:
A = 1 + 1/3 + 1/9 + 1/27 + 1/81 + 1/243 + 1/729
Nhân A với 3 ta có:
\(Ax3=3+\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}+\frac{1}{243}\)
\(\Rightarrow Ax3-S=3-\frac{1}{243}\)
\(\Rightarrow2A=\frac{2186}{729}\)
\(\Rightarrow A=\frac{2186}{729}:2\)
\(\Rightarrow A=\frac{1093}{729}\)

Bài 2Câu hỏi của nguyễn phạm mimi - Toán lớp 6 | Học trực tuyến

Bài 3

nguồn:Tính nhanh: 3/2 + 3/8 + 3/32 + 3/128 + 3/512 

Bài 4Câu hỏi của VŨ THỊ MAI CA - Toán lớp 4 - Học toán với OnlineMath

Bài 5Câu hỏi của Phạm Dora - Toán lớp 4 - Học toán với OnlineMath

Bài 6 Câu hỏi của huỳnh thị thu uyên - Toán lớp 5 - Học toán với OnlineMath

tham khảo

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 
A x 3 - A = 1 + 1/3 + 1/9 + 1/27 + 1/81 + 1/243 - (1/3 + 1/9 + 1/27 + 1/81 + 1/243 + 1/729) 
= 1 + 1/3 + 1/9 + 1/27 + 1/81 + 1/243 - 1/3 - 1/9 - 1/27 - 1/81 - 1/243 - 1/729 
= 1 - 1/729 
A x 2 = 728/729 
A = 364/729

\(\dfrac{243}{729}+\dfrac{81}{729}+\dfrac{27}{729}+\dfrac{9}{729}+\dfrac{2}{729}+\dfrac{1}{729}=\dfrac{243+81+27+9+2+1}{729}=\dfrac{363}{729}=\dfrac{121}{243}\)

anh_hung_lang_la thì làm đi

bọn kia có trả lời câu hỏi không thì bảo

1)=1023/1024

2)=1093/729

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 
A x 3 - A = 1 + 1/3 + 1/9 + 1/27 + 1/81 + 1/243 - (1/3 + 1/9 + 1/27 + 1/81 + 1/243 + 1/729) 
= 1 + 1/3 + 1/9 + 1/27 + 1/81 + 1/243 - 1/3 - 1/9 - 1/27 - 1/81 - 1/243 - 1/729 
= 1 - 1/729 
A x 2 = 728/729 
A = 364/729