mink cần gấp

reititiruit

ty từ tổ

\(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{90}\)

\(=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{9.10}\)

\(=1-\frac{1}{10}\)

\(=\frac{9}{10}\)

\(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{90}\)

= \(\frac{1}{1\times2}+\frac{1}{2\times3}+\frac{1}{3\times4}+\frac{1}{4\times5}+...+\frac{1}{9\times10}\)

= \(\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{9}-\frac{1}{10}\)

=\(\frac{1}{1}-\frac{1}{10}\)= \(\frac{9}{10}\)

2A=1+1/2+1/4+....+1/32

2A-A=(1+1/2+1/4+....+1/32)-(1/2+1/4+....+1/64)

A=1-1/64=63/64

làm đúng mà, sao tk sai mk

Dùng máy tính đấy em ơi

Đặt biểu thức trên là A ta có:

A = \(\frac{1}{3}\)+ \(\frac{1}{6}\)+ \(\frac{1}{12}\)+ \(\frac{1}{24}\)+ \(\frac{1}{48}\)+ \(\frac{1}{96}\)

A x 3 = \(1\)+ \(\frac{1}{2}\)+ \(\frac{1}{4}\)+ \(\frac{1}{8}\)+ \(\frac{1}{16}\)+ \(\frac{1}{32}\)

A x 3 = \(1\)+ \(1\)- \(\frac{1}{2}\)+ \(\frac{1}{2}\)- \(\frac{1}{4}\)+ \(\frac{1}{4}\)- \(\frac{1}{8}\)+ \(\frac{1}{8}\)- \(\frac{1}{16}\)+ \(\frac{1}{16}\)- \(\frac{1}{32}\)

A x 3 = 2 - \(\frac{1}{32}\)= \(\frac{63}{32}\)

A = \(\frac{63}{32}\): 3 = \(\frac{63}{96}\)

bằng 1

Đặt \(A=\frac{1}{3}+\frac{1}{6}+\frac{1}{12}+.....+\frac{1}{96}\)

\(\Rightarrow\frac{1}{2}A=\frac{1}{6}+\frac{1}{12}+\frac{1}{24}+.....+\frac{1}{192}\)

\(\Rightarrow A-\frac{1}{2}A=\frac{1}{3}-\frac{1}{192}\)

\(\Rightarrow\frac{1}{2}A=\frac{21}{64}\)

\(\Rightarrow A=\frac{21}{64}.2=\frac{21}{32}\)

\(\frac{95}{96}\)ko lý do