1/2+1/4+1/8+1/16+1/32=31/32

31/32 = 1/32 + 30/32 = 1/32+15/16 = 1/32 +1/16+14/16 => 
31/32 = 1/32+1/16+7/8 = 1/32+1/16 +1/8+6/8 => 
31/32=1/32+1/16 +1/8+3/4 = 1/32+1/16+1/8+1/4+2/4 = 1/32+1/16+1/8+1/4+1/2 
Vậy 31/32 = 1/32+1/16+1/8+1/4+1/2

\(\frac{31}{32}\)= \(\frac{1+2+4+8+16}{32}\)= \(\frac{1}{32}\)+ \(\frac{2}{32}\)+ \(\frac{4}{32}\)+ \(\frac{8}{32}\)+ \(\frac{16}{32}\)= \(\frac{1}{32}\)+ \(\frac{1}{16}\)+ \(\frac{1}{8}\)+ \(\frac{1}{4}\)+ \(\frac{1}{2}\)

Vậy \(\frac{31}{32}\)= \(\frac{1}{32}\)+ \(\frac{1}{16}\)+ \(\frac{1}{8}\)+ \(\frac{1}{4}\)+ \(\frac{1}{2}\)

\(\frac{31}{32}=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}\)

\(\frac{31}{32}=\frac{1}{32}+\frac{30}{32}=\frac{1}{32}+\frac{15}{16}=\frac{1}{32}+\frac{1}{16}+\frac{14}{16}\)

\(\Rightarrow\frac{31}{32}=\frac{1}{32}+\frac{1}{16}+\frac{7}{8}=\frac{1}{32}+\frac{1}{16}+\frac{1}{8}+\frac{6}{8}\)

\(\Rightarrow\frac{31}{32}=\frac{1}{32}+\frac{1}{16}+\frac{1}{8}+\frac{3}{4}=\frac{1}{32}+\frac{1}{16}+\frac{1}{8}+\frac{1}{4}+\frac{2}{4}\)

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

​Vậy :\(\frac{31}{32}=\frac{1}{32}+\frac{1}{16}+\frac{1}{8}+\frac{1}{4}+\frac{1}{2}\)

\(\frac{31}{32}=\frac{16+8+4+2+1}{32}=\frac{16}{32}+\frac{8}{32}+\frac{4}{32}+\frac{2}{32}+\frac{1}{32}=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}\)

bạn tham khảo ở đây Giúp tôi giải toán - Hỏi đáp, thảo luận về toán học - Học toán với OnlineMath

35/36= 1/2+ 1/4+ 1/9+ 1/12+ 1/36

21/20=1/2 + 1/4 + 1/5 + 1/10