\(\frac{1}{10}+\frac{1}{40}+\frac{1}{88}+...+\frac{1}{1120}\)
\(=\frac{1}{2.5}+\frac{1}{5.8}+\frac{1}{8.11}+...+\frac{1}{32.35}\)
\(=\frac{1}{3}\left(\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+...+\frac{1}{32}-\frac{1}{35}\right)\)
\(=\frac{1}{3}\left(\frac{1}{2}-\frac{1}{35}\right)=\frac{33}{140}\)
ta thấy :
1/10=1/2x5
1/40=1/5x8
1/88=1/8x11
.......
1/1908=29x32
1/1120=1/32x35
ta có:
1/10+1/40+1/88+....+1/908+1/1120
=1/2x5+1/5x8+..........+1/29x32+1/32x35
=3/3x(1/2x5+1/5x8+..........+1/29x32+1/32x35)
=1/3x(3/2x5+3/5x8+..........+3/29x32+3/32x35)
=1/3x(1/2-1/5+1/5-1/8+...........+1/29-1/32+1/32-1/35)
=1/3x(1/2-1/35)
=1/3x33/70=11/70
hùng sai rồi
1/2-1/35=35/70-2/70=33/70x1/3=11/70
