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

C=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

C=1-1/128

C=127/128

D=1/2+1/6+1/12+1/20+1/30+1/42

D=1/1.2+1/2.3+1/3.4+1/4.5+1/5.6+1/6.7

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

D=1/1-1/7

D=6/7

\(B=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}\)

\(2B=1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}\)

\(2B-B=1-\frac{1}{64}\)

\(B=\frac{63}{64}\)

A=1/1*2+1/2*3+1/3*4+1/4*5+1/5*6+1/6*7

=1-1/2+1/2-1/3+1/3-1/4+1/4

=1/5+1/5-1/6+1/6-1/7

=1-1/7

=6/7

cauB tương tự bạn tự làm nhé 

CHÚC BẠN HỌC TỐT

A = 1/2 + 1/6 + 1/12  + 1/20 + 1/ 30 + 1/42

   = \(\frac{1}{1x2}+\frac{1}{2x3}+\frac{1}{3x4}+\frac{1}{4x5}+\frac{1}{5x6}+\frac{1}{6x7}\)

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

   =\(1-\frac{1}{7}\)

   = \(\frac{6}{7}\)

Ủng hộ mình nha căm ơn nhiều

a)Đặt \(A=\dfrac{6}{1.4}+\dfrac{6}{4.7}+\dfrac{6}{7.10}+...+\dfrac{6}{97.100}\)

\(3a=3-\dfrac{3}{4}+\dfrac{3}{4}-\dfrac{3}{7}+\dfrac{3}{7}-\dfrac{3}{10}+...+\dfrac{3}{97}-\dfrac{3}{100}\)

\(=3-\dfrac{3}{100}\)

\(=\dfrac{297}{100}\)

b)Đặt \(B=\dfrac{4}{1.3}+\dfrac{16}{3.5}+\dfrac{36}{5.7}+...+\dfrac{9604}{97.99}\)

\(=2b=\dfrac{2}{1.3}+\dfrac{2}{3.5}+\dfrac{2}{5.7}+...+\dfrac{2}{97.99}\)

\(2b=2-\dfrac{2}{3}+\dfrac{2}{3}-\dfrac{2}{5}+\dfrac{2}{5}-\dfrac{2}{7}+...+\dfrac{2}{97}-\dfrac{2}{99}\)

\(2b=2-\dfrac{2}{99}=\dfrac{198}{99}-\dfrac{2}{99}=\dfrac{196}{99}\)

c) Tương tự! Bạn tự làm nhé!

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

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

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

A = 1/2 + 1/4 + 1/8 + ... + 1/128

A = 1/2^1 + 1/2^2 + 1/2^3 + ... + 1/2^7

2A = 1 + 1/2 + 1/2^2 + ... + 1/2^6

2A - A = 1 - 1/2^7 = A

G = 5 - 5^2/1*6  5^2/6*11 - ... - 5^2/101*106

G = -5(-1 + 5/1*6 + 5/6*11 + ... + 5/101*106)

G = -5(-1 + 1 - 1/6 + 1/6 - 1/11 + ... + 1/101 - 1/106)

G = -1.(-1/106)

G = 1/106

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

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

\(2A-A=1-\frac{1}{128}\)

\(A=\frac{127}{128}\)