1/2+1/4+1/8+1/10+1/16+1/32+1/64+1/128

=1-1/2+1/2-1/4+1/4-1/6+1/6-1/8+1/8-1/16+1/16-1/32+1/32-1/64+1/64-1/128+1/128

=1-1/128

=127/128

#Sagittarius#

 Ta có 1/11; 1/12; 1/13;...; 1/39 > 1/40

\(\Rightarrow\) A = 1/11 + 1/12 + 1/13 +...+ 1/39 +1/40 > 1/40 + 1/40 + 1/40 +...+ 1/40 + 1/40(có 30 số hạng)

         A > 30/40

   Mà 30/40 =3/4 nên A >3/4

          Vậy A > 3/4

#)Giải :

Gọi tổng trên là A

\(A=\frac{3}{1.4}+\frac{3}{4.7}+\frac{3}{7.10}+...+\frac{3}{40.43}\)

\(A=3-\frac{3}{4}+\frac{3}{4}-\frac{3}{7}+\frac{3}{7}-\frac{3}{10}+...+\frac{3}{40}-\frac{3}{43}\)

\(A=3-\frac{3}{43}\)

\(A=3\frac{3}{43}=\frac{132}{43}\)

     #~Will~be~Pens~#

       Câu hỏi của Nguyễn Hữu Hưng       

\(\frac{1}{5.8}+\frac{1}{8.11}+...+\frac{1}{x.\left(x+3\right)}=\frac{101}{1540}\)

\(\frac{3}{5.8}+\frac{3}{8.11}+...+\frac{3}{x.\left(x+3\right)}=\frac{303}{1540}\)

\(\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+...+\frac{1}{x}-\frac{1}{x+3}=\frac{303}{1540}\)

\(\frac{1}{5}-\frac{1}{x+3}=\frac{303}{1540}\)

\(\frac{1}{x+3}=\frac{1}{308}\)

\(\Rightarrow x+3=308\)

\(x=305\)

\(\frac{4}{5}+\frac{2}{7}+\frac{11}{5}+\frac{12}{7}+\frac{1}{5}\)

\(=\frac{4}{5}+\frac{11}{5}+\frac{1}{5}+\frac{2}{7}+\frac{12}{7}\)

\(=\frac{4+11+1}{5}+\frac{2+12}{7}\)

\(=\frac{16}{5}+\frac{14}{7}\)

\(=\frac{16}{5}+2=\frac{26}{5}\)

\(\frac{4}{5}+\frac{2}{7}+\frac{11}{5}+\frac{12}{7}+\frac{1}{5}\)

\(=\left(\frac{4}{5}+\frac{11}{5}+\frac{1}{5}\right)+\left(\frac{2}{7}+\frac{12}{7}\right)\)

\(=\frac{16}{5}+\frac{14}{7}\)

\(=\frac{16}{5}+2=\frac{16}{5}+\frac{10}{5}=\frac{26}{5}\)

\(\frac{4}{5}+\frac{2}{7}+\frac{11}{5}+\frac{12}{7}+\frac{1}{5}\)

\(=\left(\frac{4}{5}+\frac{11}{5}+\frac{1}{5}\right)+\left(\frac{2}{7}+\frac{12}{7}\right)\)

\(=\frac{16}{5}+2\)

\(=\frac{26}{5}\)

\(\frac{1}{5.8}+\frac{1}{8.11}+\frac{1}{11.14}+...+\frac{1}{x.\left(x+30+\frac{101}{1540}\right)}\)

Phải gì không .

ghi nham la the nay

1 phan 5 nhan 8 cong 1 phan 8 nhan 11 cong 1 phan 11 nhan 14 +..........+1 phan x nhan (x+3)=101 phan 1540