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Ta có :
\(\left(1+\frac{1}{3}+\frac{1}{5}+\frac{1}{7}+\frac{1}{9}\right)-\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{6}+\frac{1}{8}+\frac{1}{10}\right)\)
\(=\left(1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{9}+\frac{1}{10}\right)-2\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{6}+\frac{1}{8}+\frac{1}{10}\right)\)
\(=\left(1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{9}+\frac{1}{10}\right)-\left(1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}\right)\)
\(=\frac{1}{6}+\frac{1}{7}+\frac{1}{8}+\frac{1}{9}+\frac{1}{10}\left(đpcm\right)\)
=1/1x2 + 1/2x3 + 1/3x4 +1/4x5+ 1/5x6 + 1/6x7 + 1/7x8 + 1/8x9 + 1/9x10
=1/1 -1/2 +1/2 -1/3 +1/3 -1/4+1/4-1/5+ 1/5 -1/6 + 1/6-1/7 + 1/7-1/8 + 1/8- 1/9 + 1/9- 1/10
=1/1 -1/10
=9/10
\(1+\frac{1}{3}+\frac{1}{5}+\frac{1}{7}+\frac{1}{9}-\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{6}+\frac{1}{8}+\frac{1}{10}\right)\)
\(=1+\frac{1}{2}+...+\frac{1}{10}-2\left(\frac{1}{2}+\frac{1}{4}+...+\frac{1}{10}\right)\)
\(=1+\frac{1}{2}+...+\frac{1}{10}-\left(1+\frac{1}{2}+...+\frac{1}{5}\right)\)
\(=\frac{1}{6}+\frac{1}{7}+...+\frac{1}{10}\)
Ta có:
1/1*2+1/2*3+1/3*4+1/4*5+1/5*6+1/6*7+1/7*8+1/8*9+1/9*10
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8+1/8-1/9+1/9-1/10
=1-1/10
=9/10
1+1+1+1+1+1+1+1+1+1=10
1+1+1+1+1+1+1+1+1-1=9
1+1+1+1+1+1+1+1-1-1=8
1+1+1+1+1+1+1-1-1-1=7
1+1+1+1+1+1-1-1-1-1=6
1+1+1+1+1-1-1-1-1-1=5
1+1+1+1-1-1-1-1-1-1=4
1+1+1-1-1-1-1-1-1-1=3
1+1-1-1-1-1-1-1-1-1=2
1-1-1-1-1-1-1-1-1-1-1=0
Nối cung ta điền dấu cộng hết
Các số còn lại ta giảm mỗi số một dấu cộng = dấu -