1/1.4+1/4.7+1/7.10+1/10.13+1/13.16

=1/3.(3/1.4+3/4.7+3/7.10+3/10.13+3/13.16)

=1/3.(1/1-1/4+1/4-1/7+1/7-1/10+1/10-1/13+1/13-1/16)

=1/3.(1/1-1/16)

=1/3.(16/16-1/16)=1/3.15/16=5/16

\(a,\frac{1}{6}+\frac{1}{12}+\frac{1}{24}+....+\frac{1}{384}\)

\(\text{Đ}\text{ặt}\)\(A=\frac{1}{6}+\frac{1}{12}+\frac{1}{24}+...+\frac{1}{384}\)

\(2A=\frac{1}{3}+\frac{1}{6}+\frac{1}{12}+....+\frac{1}{192}\)

\(2A-A=\frac{1}{3}-\frac{1}{384}\)

a đề sai

b)Đặt A=1/4x7 + 1/7x10 + 1/10x13 +...........+ 1/19x22

\(3A=3\left(\frac{1}{4.7}+\frac{1}{7.10}+...+\frac{1}{19.22}\right)\)

\(3A=\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{19}-\frac{1}{22}\)

\(3A=\frac{1}{4}-\frac{1}{22}\)

\(A=\frac{9}{44}:3\)

\(A=\frac{3}{44}\)

E= 7/4x7 + 7/7x10 =7/10x13+...+ 7/301x304

\(=\frac{7}{3}\left(\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{301}-\frac{1}{304}\right)\)

\(=\frac{7}{3}\left(\frac{1}{4}-\frac{1}{304}\right)\)

\(=\frac{7}{3}\cdot\frac{75}{304}\)

\(=\frac{175}{304}\)

E = \(\frac{7}{4.7}+\frac{7}{7.10}+\frac{7}{10.13}+...+\frac{7}{301.304}\) 

   =\(\frac{7}{3}.\frac{7-4}{4.7}+\frac{7}{3}.\frac{10-7}{7.10}+\frac{7}{3}.\frac{13-10}{10.13}+...+\frac{7}{3}.\frac{304-301}{301.304}\)

 = \(\frac{7}{3}.\left(\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+\frac{1}{10}-\frac{1}{13}+...+\frac{1}{301}-\frac{1}{304}\right)\)=\(\frac{7}{3}.\left(\frac{1}{4}-\frac{1}{304}\right)=\frac{7}{3}.\frac{75}{304}=\frac{175}{304}\)

=1/1-1/4+1/4-1/7+1/7-1/10+1/10-1/13+1/13-1/16

=1-1/16=15/16

Bài 2 :

Ta có :

\(A=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}=\left(1-\frac{1}{2}\right)+\left(\frac{1}{2}-\frac{1}{4}\right)+\left(\frac{1}{4}-\frac{1}{8}\right)+\left(\frac{1}{8}-\frac{1}{16}\right)+\left(\frac{1}{16}-\frac{1}{32}\right)\)

    \(=1-\frac{1}{32}\)

và \(B=\frac{2003}{2004}=1-\frac{1}{2004}\)

Vì \(\frac{1}{32}>\frac{1}{2004}\) nên A < B

A<B

Ta có:

A = \(\frac{5}{4.7}+\frac{5}{7.10}+\frac{5}{10.13}+...+\frac{5}{301.304}\)

A = 5. (\(\frac{1}{4.7}+\frac{1}{7.10}+\frac{1}{10.13}+...+\frac{1}{301.304}\))

3A = 3.5. (\(\frac{1}{4.7}+\frac{1}{7.10}+\frac{1}{10.13}+...+\frac{1}{301.304}\))

3A = 5. (\(\frac{3}{4.7}+\frac{3}{7.10}+\frac{3}{10.13}+...+\frac{3}{301.304}\))

3A = 5. ( \(\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+\frac{1}{10}-...-\frac{1}{301}+\frac{1}{301}-\frac{1}{304}\))

3A = 5. ( \(\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+\frac{1}{10}-...-\frac{1}{301}+\frac{1}{301}-\frac{1}{304}\))

3A = 5. ( \(\frac{1}{4}-\frac{1}{304}\))

3A = \(\frac{5.75}{304}\)

3A = \(\frac{375}{304}\)

A= \(\frac{125}{304}\) . Vậy: A = \(\frac{125}{304}\)

Chúc bạn học tốt! Tick cho mình nhé!

3/(1×4)+3/(4×7)+3/(7×10)+3/(10×13)+3/(13×16)

=1-1/4+1/4-1/7+1/7-1/10+1/10-1/13+1/13-1/16

=1-1/16

=15/16

31 x 434 x 737 x 10310 x 13 = 1.3289876e+12

mik phải dùng máy tính chứ có sịp nhân mới trả lời đc 

nhỉ ?????

ko có 3/13x16 nha bn