1/1.3-2/3.5+3/5.7-4/7.9+5/9.11-6/11.13+7/13.15-8/15.17

Đáp án:

Giải thích các bước giải:

1/1.3-2/3.5+3/5.7-4/7.9+5/9.11-6/11.13+7/13.15-8/15.17

=1/4.(4/1.3-8/3.5+12/5.7-16/7.9+20/9.11-24/11.13+28/13.15-32/15.17)

=1/4.(3+1/1.3-5+3/3.5+7+5/5.7-9+7/7.9+11+9/9.11-13+11/11.13+15+13/13.15-17+15/15.17

=1/4.[(1+1/3)-(1/3+1/5)+(1/5+1/7)-(1/7-1/9)+...-(1/15+1/17)]

=1/4.(1+1/3-1/3-1/5+1/5+...-1/17)

=1/4.(1-1/17)=1/4.16/17=4/17

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