Đáp án+Giải thích các bước giải:
20. A=1/2+5/6+11/12+...+9899/9900
A=(1-1/2)+(1-1/6)+(1-1/12)+....+(1-1/9900)
=99-(1/2+1/6+1/12+...+1/9900)
=99-(1/1.2+1/2.3+1/3.4+....+1/99.100)
=99-(1-1/2+1/2-1/3+1/3-1/4+....+1/99-1/100)
=99-(1-1/100)
=99-99/100
=9801/100
23. A=2/3+14/15+34/35+...+9998/9999
=(1-1/3)+(1-1/15)+(1-1/35)+...+(1-1/9999)
=50-(1/3+1/15+1/35+....+1/9999)
=50-1/2(2/1.3+2/3.5+2/5.7+....+2/99.101)
=50-1/2(1-1/3+1/3-1/5+1/5-1/7+....+1/99-1/101)
=50-1/2(1-1/101)
=50-50/101
=5000/101
26. A=9/10+39/40+....+1119/1120
=(1-1/10)+(1-1/40)+...+(1-1/1120)
=11-(1/10+1/40+...1/1120)
=11-1/3(3/2.5+3/5.8+...+3/32.35)
=11-1/3(1/2-1/5+1/5-1/8+...+1/32-1/35)
=11-1/3(1/2-1/32)
=11-5/32
=347/32
