a: \(A=\dfrac{1}{2}+\left(\dfrac{1}{2}\right)^2+\left(\dfrac{1}{2}\right)^3+...+\left(\dfrac{1}{2}\right)^7\)

=>\(2\cdot A=1+\dfrac{1}{2}+\left(\dfrac{1}{2}\right)^2+...+\left(\dfrac{1}{2}\right)^6\)

=>\(2A-A=1-\left(\dfrac{1}{2}\right)^7=1-\dfrac{1}{128}=\dfrac{127}{128}\)

=>\(A=\dfrac{127}{128}\)

b: \(B=\dfrac{1}{1\cdot2}+\dfrac{1}{2\cdot3}+...+\dfrac{1}{10\cdot11}\)

\(=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{10}-\dfrac{1}{11}\)

\(=1-\dfrac{1}{11}=\dfrac{10}{11}\)

1/6 + 1/12 + 1/20 + 1/30 + 1/42 + 1/56 
= 1/2x3 + 1/3x4 + 1/4x5 + 1/5x6 + 1/6x7 + 1/7X8 
=1/2 - 1/3 + 1/3 -1/4 + 1/4 - 1/5 + 1/5 -1/6 + 1/6 - 1/7 + 1/7 - 1/8 
= 1/2 - 1/8 
= 4/8 - 1/8 
= 3/8 

\(\frac{3}{8}\)nha bạn

3/8 đó bạn

A=1/20+1/30+1/42+1/56+1/72+1/90

A=1/4x5+1/5x6+1/6x7+1/7x8+1/8x9+1/9x10

A=1/4-1/5+1/5-1/6+...+1/9-1/10

A=1/4-1/10

A=3/20

Ban oi,toan nay khong phai toan lop 4

có ai trả lời ko

\(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}\)

\(=\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}\)

\(=\frac{3-2}{2.3}+\frac{4-3}{3.4}+\frac{5-4}{5.4}+\frac{6-5}{5.6}+\frac{7-6}{7.6}+\frac{8-7}{7.8}\)

\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}\)

\(=\frac{1}{2}-\frac{1}{8}=\frac{4}{8}-\frac{1}{8}=\frac{3}{8}\)

A=1/20+1/30+1/42+1/56+1/72+1/90

A=1/4.5+1/5.6+1/6.7+1/7.8+1/8.9+1/9.10

A=1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8+1/8-1/9+1/9-1/10

A=1/4-1/10

A=3/20

minh ko biet :>

 1/2 + 1/6 + 1/12 + 1/20 + 1/30 + 1/42 + 1/56 + 1/72 + 1/90 
=1/(1.2)+1/(2.3)+1/(3.4)+1/(4.5) 
+1/(5.6)+1/(6.7)+1/(7.8) 
+1/(8.9)+1/(9.10) 
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5.+1/5-1/6... 
+1/9-1/10 
=1-1/10 
=9/10

1/6+1/12+1/20+1/30+1/42+1/56

=1/2x3+1/3x4+1/4x5+1/5x6+1/6x7+1/7x8

=1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8

=1/2-1/8

=3/8

\(=\frac{1}{2.3}+\frac{1}{3.4}+....+\frac{1}{11.12}\)

\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{11}-\frac{1}{12}\)

\(=\frac{1}{2}-\frac{1}{12}\)

\(=\frac{5}{12}\)

bn sẽ tinh theo kieeuranhaan 2 nha xin lỗi mik làm bi này rùi nhưng mik quên mik có sacks xem lại