\(A=\frac{1}{4}+\frac{1}{12}+\frac{1}{36}+...+\frac{1}{972}+\frac{1}{2916}\)

\(3A=\frac{3}{4}+\frac{1}{4}+\frac{1}{12}+...+\frac{1}{324}+\frac{1}{972}\)

\(3A-A=\left(\frac{3}{4}+\frac{1}{4}+\frac{1}{12}+...+\frac{1}{324}+\frac{1}{972}\right)-\left(\frac{1}{4}+\frac{1}{12}+\frac{1}{36}+...+\frac{1}{972}+\frac{1}{2916}\right)\)

\(2A=\frac{3}{4}-\frac{1}{2916}\)

\(A=\frac{1093}{2916}\)

rút gon xuống 1/4 rồi laays1/4 nhân tất cả là ra

820/2187

3xB=3x(1/4+1/12+1/36+1/108+1/324+1/972+1/2916+1/8748)

3xB=3/4 + 1/4 +1/12 +1/36 +.........+1/2916

3xB - B= (3/4 + 1/4 + 1/12+1/36 + .........+1/2916) - ( 1/4 +1/12 +1/36 +1/108 + 1/324 + 1/972 + 1/2916 +1/8748 )

2xB =3/4 - 1/8748

2xB =1640/2187

B = 1640/2187 :2

B = 820/2187.

mình có cách làm như bn Kaito Kid và = 820/2187

1/2 + 1/4 + 1/8 … + 1/256 + 1/512

= 1 - 1/2 + 1/2 - 1/4 + 1/4 - 1/8 + … + 1/128 - 1/256 + 1/256 - 1/512

= 1 - 1/512

= 512/512 - 1/512

= 511/512

Ghi chú: Mình chỉ làm được câu a thôi, xin lỗi bạn nha 😅😅😅

Chúc bạn học tốt.

😁😁😁

cảm ơn bn

1093/2916

A  =  \(\frac{1093}{2916}\)

< nhe 

to nhanh nhat hay tk va kb nhe

Lời giải:

$S=4+12+36+108+....+972+2916$

$3\times S=12+36+108+324+...+2916+8748$

$3\times S-S=(12+36+108+324+...+2916+8748)-(4+12+36+108+....+972+2916)$

$2\times S=8748-4=8744$

$S=8744:2=4372$