Question

a)\(\frac{3}{5x8}+\frac{3}{8x11}+...+\frac{3}{2006x2009}\)

b)\(\frac{1}{6x10}+\frac{1}{10x14}+...+\frac{1}{402x406}\)

c)\(\frac{10}{7x12}+\frac{10}{12x17}+...+\frac{10}{502x507}\)

Ai làm nhanh nhất mk sẽ tick cho.Mk đag cần gấp.Mong các bn giúp đỡ

Answer 1

a,A=1/5-1/8+1/8-1/11+...+1/2006-1/2009=1/5-1/2009=2004/10045

b,B=1/4x(4/6x10+4/10x14+...+4/402x406)

=1/4x(1/6-1/10+1/10-1/14+...+1/402-1/406)

=1/4x(1/6-1/406)

=1/4x100/609=25/609

c,C=2x(5/7x12+5/12x17+...+5/502x507)

=2x(1/7-1/12+1/12-1/17+...+1/502-1/507)

=2x(1/7-1/507)

=2x500/3549

=1000/3549

Xin lỗi vì ko viết được rõ ràng.Mong bạn thông cảm. Chúc bạn học tốt.

  

Answer 2

\(\frac{3}{5\times8}+\frac{3}{8\times11}+...+\frac{3}{2006\times2009}\)

\(=\frac{1}{3}\left(\frac{3}{5\times8}+\frac{3}{8\times11}+...+\frac{3}{2006\times2009}\right)\)

\(=\frac{1}{3}\left(\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+...+\frac{1}{2006}-\frac{1}{2009}\right)\)

\(=\frac{1}{3}\left(\frac{1}{5}-\frac{1}{2009}\right)\)

\(=\frac{1}{3}\left(\frac{1}{5}-\frac{1}{2009}\right)\)

\(=\frac{1}{3}\left(\frac{2009}{10045}-\frac{5}{10045}\right)\)

\(=\frac{1}{3}.\frac{2004}{10045}=\frac{2004}{30135}\)